Sword  Art Side Story:
Several times over the course of PSO2, other characters from other games have appeared. Usually though, they appear for show, and hand out a few little prize quests and chat up a sentence or two. Some crossovers were also limited to giving the costumes to your character like Guilty Gear, for example. However, when Sword Art Online (That anime show) crossed over, it did have quite a bit of plot about it so it appears here. It doesn't have anything particularly new for the PSO2 plot side, but it does reiterate some important parts and confirm some things. Also, if you liked SAO / Kirito and all them, this would certainly be something good for you to read.
Whatever SAO did for PSO2, it had to have been a lot, this is by far the largest crossing over it ever had (and with the game 'finished now', it will keep the crown forever--) even over their own other games that they apparently made vague hand-wave attempts to cross in like putting Laia Martinez & Red Ring Rico in as NPCs. (Which in RRR's case is offensive, she's dead--that's the point of her so dragging her corpse out and puppeting it to do 'look what we can do aren't you nostalgic' was never the right move.)

But what is Sword Art Online?
Briefly...It was one of the first shows in the "Isekai" genre, which is generally that "A person goes to another world & has to do things, generally becoming a hero or villain of some sort along the way". It did the job pretty well and so it was a popular show that branched out into other shows. The premise was that there was a video game called Sword Art Online, but you basically had to buy a big thing that you plugged your actual BRAIN into the game and so it felt like it was real/you were really there. Of course, something goes "horribly wrong TM" and predictably 'everyone's trapped in the game and the only way out is to beat it! And if you die in the game you die for reeeeeeeellll OoooOooOo"
The problem with it being that the person who goes to another world very easily becomes a Mary Sue and things can get predictable fairly quickly. The premise is interesting but hard to execute without Mary Sues or trite themes. Kirito himself falls a bit into 'trite' because he is a beige kid with black hair and dark gray eyes EX: he is identical to like...way too many people. The challenge that SAO did actually rise to was making the journey & characters interesting enough to hold everyone's attention to become the success that it was.

When you enter the shop lobby, a scene with Matoi will appear. A cast and a ranger woman have gotten a handshake from Matoi. She explains lots of people have been coming up to her lately to say CG, and that everyone admires the Guardians but it’s mostly thanks to you. She wants to find somewhere quiet to have lunch so we can…

But, she is interrupted by a long hair girl dressed in white. She is beige with quite long middle-brown hair and brown eyes. It labels her as ‘girl in knight’s armor’, but she’s…kinda not because she has exposed shoulders, strapped on white sleeves, and a regular looking outfit. Yes it has a small metallic chest plate just over the boob-area but…there’s no armor on her. She asks if you’ve got a minute. She wants to ask a few questions. Are you Guardians? Matoi says yes but who are you? She says her name is Asuna, and she just started today. As soon as she ‘logged in’ she got out here without any sort of tutorial.

Matoi doesn’t know what is a newbie, nor knows about any sort of tutorial. Asuna agrees with her confusion, saying she’s talked to people ever since arriving in the world. All of them react how Matoi did. But, they also said if you run into a problem, talk to a Guardian. Matoi says as an aside to you, that if she’s in trouble, we should do everything to help.

Let’s Hear Her Out For Now
If She Needs Our Help, We Have No Choice.

If you say Let’s Hear Her Out For Now , Matoi will agree to help. She’ll reintroduce herself, and Matoi intros the 2 of you. She then mentions Kirito, who has come along with her. Now, a young looking guy appears. He is beige in color just as she is, but with black hair and very dark gray eyes. He’s wearing a black shirt with black open coat over it that has a sort of tri-belt on the chest area. He asks if you’ve been playing a game for long?

Matoi asks about a game?
He … at her and asks about the world and what sort of a place it is. She gives the usual, which is this is the ARKS ship in the Oracle fleet and we’re the planetary investigation team, so wouldn’t you say that’s accurate?

That Was Perfect
I Don’t Think That’s What He Was Asking

If you say That Was Perfect, Matoi will nod and say right, but why ask such things about something everyone already knows? Dissapointed, seemingly he … her again and says he sees. He thanks her, and says they’ll take a look around the world a bit longer. She ‘huh’ at them, so he says if there’s anything else they don’t understand, they’ll give a shout, so please help us then. Matoi looks like she’ll ask something else, but Kirito tells Asuna let’s go so she says bye. They then leave. Matoi calls them a curious bunch.

Xiera cuts in to confirm that they weren’t ARKS. This startles Matoi, so she explains they came here from Earth thru the stupid, never explained and badly plotted PSO2 /game interface. Matoi remembers that it was the game popular with Hitsugi and all. Xiera confirms that it was Mother who created that interface & made it like a game, to get herself/minions/Earth people into this dimension with us ARKS so she could take her revenge against the Photoners who created the ARKS.
It used to be that anyone capable (OF WHAT???) could come to this world through it but access is now limited to those with proper clearance. Of course, did those 2 have it? Enga in Earth Guide hasn’t contacted Xiera about it. It bothers her (as well it should) so she’s going to contact him about it. Meanwhile, can you keep an eye on them and keep them out of trouble? They seem to think they’re in a game, so who knows what might happen. Matoi says it sounds like a mission, but she’ll do the best. But…how did Xiera know what was going on when she contacted us just now? That’s easy, when she heard Guardians are out for a stroll, she thought she’d sneak a peek…but! Matoi exclaims about her watching us. She then says the rest is up to you so over and out! At this she is nervous because she has confessed to watching people again. This is another instance of Xiera peeping at people. It is in character but never gets explained as to why she likes to spy on others.

The scene ends.

Elsewhere in the lobby, in a scene your character couldn't possibly see Asuna asks Kirito that the people we just met weren’t NPCs, right? He thinks they’re not also, but it doesn’t mean they are players because they don’t feel the world is a game. They treat it as if it’s the real world they live in. She agrees and says ‘our outfits’. Even though we converted from ALO we are in our SAO gear. He thinks that’s evidence that it’s no ordinary game, but the logout! They wave their hand to reveal the menu you see at the bottom of the screen, but hovering in front of them. She says that they should be able to leave. He feels that means no major danger is here. They wipe their menus down, and he says a lot of stuff doesn’t sit right with him, but we did go to the trouble of converting so we should at least take a look around. We should figure out the fighting first. The gear and outfits on people we have passed has caught her eye. We should try asking Matoi where all the good vendors are.

The scene ends.

This causes Kirito to appear as an NPC in the lobby. His quest for you is Why Don’t We Dive Together. Matoi and Asuna are shopping, so he calls going into the forest ‘a dive’. Taking it will give you his partner card so you can go to the Forest, as he’s more interested in combat than shopping. What is a Dive? It's what they called plugging your brain into the SAO game.

Completeing Forest Free Field with Kirito in the party on any difficulty will give you:
Seeing Something Wonderful With: Asuna & Matoi in Skyscape Free Field
To finish this, you just have to beat Skyscape Free Field with Asuna & Matoi in the party on any difficulty. They have little untranslated chat phrases they let out along the way, but it's nothing for the plot. When finished, Asuna says thanks for showing such a cool view (as is the usual) but Matoi will chime in on the cut in chat thing. She had a great time too and is glad the 3 of you went. Asuna then says if only she could see the view with the one she loves like how Matoi did. Matoi clarifies that your char and her are partners but does that mean the one Asuna likes is…Kirito? she confirms it with a simple ‘yeah its him’. When she looks at him, no matter what darkness she’s facing, he’ll always be there to rescue her because that’s the kind of guy he is. Matoi confesses that your char saved her from the darkness (that is actual literally too) so in that, we’re the same way. Asuna is glad to be friends with Matoi, and they should talk more.

This gives you Kirito’s order Grind A Weapon
He’ll say Asuna’s in a good mood since getting back from the quest, she’s happy to have made friends so thank you for that. He wants to upgrade his items, but feels its complicated so the best way to learn is to watch you do it. When you do, he’ll say to strengthen weapons before going out is important and he wants to take his to the limit. Lots of ARKS seem to hate the clerks, but he feels sorry for them. He feels the quest was helpful, but now all he has to do is get a powerful weapon to take there and upgrade…but that’s the hard part. He is clearly referring to the 'RNG=random number generator" powered way of grinding with clerk Dudu (his name likely wasn't an accident) which--why if everyone hates it do they keep putting the mechanic into the game?  Finishing this gives you Asuna’s order

Craving Something Wild:
You have to bring her a Seafood Brochette. She wants to learn to make it with Tunnel Piranha, Shironia Mussel and Caves Char.  She has heard about Oracle’s dishes from Matoi, and wants to try to cook up something. Could you teach her a recipe? Matoi’s favorite was Seafood Brochette. You obviously tell her she ought to try eating it before you give her the recipe. So, she’ll ask you to bring her one. Having one in inventory will complete the quest, so she’s surprised you got it so quickly and will try it. She thinks it’s simple but delicious. She says you’re a good cook too. She now understands the recipe and will cook it for Kirito, it’ll be a surprise. She thanks you for your time, but is still learning the ingredients. She hopes to one day be able to cook up a banquet. This gives you Kirito’s order A Double Date

A Double Date with Kirito, Asuna & Matoi.
He wants to try a 4 person party. There’s already you, Asuna & Him but…Asuna will chime in saying ask for Matoi, silly, it’s about all 4 of us together. He laughs, says sure, but he hates to have to keep leaning on you so next time he’ll make up for it. The quest is to beat Shironia Exploration.

Once you do, they’ll chat again. Kirito understands the value of 4 member parties, everyone agrees it was fun, and Asuna wants to go shopping with Matoi again and invites you along. Kirito though, wants to ask you something instead. He’s happy with his current class but wants to ask you about other classes more later on. This gives you his next order

Advice on Getting Stronger
You have to find and talk to Stratos, Kyokuya and Lucotte. He feels asking the successor class reps will be the best way to find out how to get stronger. Going to Lucotte, she’ll say ‘master’ has told her about Kirito so in her experience…KNOW with whom you are dealing READ what they plan to do and ENJOY yourself as you do it. All 3 are important if even one is lacking you’ll struggle. Kirito interperates it as KNOW the enemy strengths, READ the tells for the attacks and ENJOY the battle? She agrees, saying those are the ways of the Maid. Master them and the hospitality you provide will be without peer.
Kirito surprises at this, the way of the Maid? He thought she was telling him how to get stronger. Now she frets and apologizes for being rude, she’d thought he was looking for tips on how he can become a better maid. Kirito thinks it over though, and says they could actually come in handy, it really was very helpful. She is then happy.

Talking to Stratos:
You tell her a friend has a question for her. Ideally, the answer is training every day but more importantly you need a role model to follow. He can’t think of anybody, though. She wonders about that because she became an ARKS is because there was someone she wanted to be like. She had a hero, so she wanted to be a hero to someone else. But, it’ll be different for each person, if you can’t think of anyone to admire, maybe there’s someone you want to beat? He considers this helpful because there may be someone like that. (Possibly in the show)

Talking to Kyokuya
He guesses a man you’ve talked to recently has put you up to asking him something. Kirito wonders about ‘put up to’. Now talking to Kyokua…will usually set him forth on one of his edgelord rants and this is no different calling poor Kirito a ‘litlte man who wants power’, so the BlackWolf (Yes that is him referring himself in 3^rd person) will teach him the true meaning of the word which is the horrifying power of the Phantom. Somehow, he is able to put pointy brackets around this word! In his speech! Edgy pointy brackets! True power comes from emptiness if ever you hold something precious to you, something that you can’t afford to lose, then that becomes your weakness. Light illuminates darkness but darkness cannot conceal light. One such as himself, who’s hands are already steeped in darkness has no right to attempt to grasp the light. Those who seek to have everything, lose everything.

But, as an aside to you, on the subject of ‘that man’ (meaning Kirito) he’s sensed something about him. Does he really believe that Black Cloak Eternal Night that he is wearing (that’s the name that Kyokua has given to Kirito's trench coat get-up with the belt topper thing--it has no name in Oracle/ARKS ships because it is not ARKS made, Kyokua is making up its name right here on the spot.) will make him worth of the power of Phantom?
Kirito has been on the cut in call this whole time anyway so of course he will answer that he uh….doesn’t think his outfit’s called anything like that and he doesn’t really get what he was talking about but he’ll guess that it might be helpful? You can then leave. Kyokua is hilariously unhelpful here, mostly. Of course, you can buy Kirito's outfit in pso2, but it's called Kirito's Outfit, not Kyokua's name for it.

Turning in the order, he says the answers weren’t exactly what he was expecting but he can use what he’s got. He was surprised at how…unique…they all were. Are all the class reps that way? Getting a variety of perspectives is a good thing so he’ll thank them in person next time. In the end though, he’ll have to figure out the best way to become stronger himself, so thanks for your help.

He has thought it over and their advice adds up to the teachings of a warrior. It applies as well to any world, so in other words…he feels he can put the experiences he’s gained so far to good use here. Where we came from, it was really important to use coordinated attacks to take down big enemies. So, would it be effective here too? Can his & Asuna coordination surpass you two? (Matoi & you) To lend them a hand, will you accept their challenge? Just then, Asuna & Matoi return. He says WB, your timing is great. We were talking about a match pitting 2 vs 2.

Let’s Do It
What Do You Think Matoi?

If you ask What Do You Think Matoi? She’d love to, a real battle with Asuna. But, actually fighting each other could be dangerous so let’s see who can defeat the most enemies. Kirito agrees. She won’t hold back so let’s both do our best! Asuna asks Kirito let’s make sure it’s us 2 that wins. He hopes the Guardians are prepared. They choose:

Successive Practice Harkotan:
So, you have to go there with Matoi and beat this timed quest. But, you can choose any difficulty you want to run on. This type of quest gives no EXP and is in a single room/arena area where you have to defeat a certain number of enemies (100) in time (to get the grade) You have to finish with Asuna Matoi & Kirito.

When you do…They ask what’s the score, did we win? They were 2 short…but it was a photo finish and we’ll catch up to you some day. Getting near them to turn the quest in will trigger a scene in the upper lobby with all 3. Kirito says since they were only 2 behind, you 2 are the real deal. But, we made good use of switching so good job Matoi. Matoi says you too, there were many times she was convinced we’d lose because you 2 were in perfect sync. Asuna says they’ve been fighting along side ach other for a long time. Kirito says it was plenty of good and bad together. Asuna keeps insisting that you 2 are a great couple, which flusters up Matoi again. She questions A couple…?! We’re not at that stage yet…right?

Now, you can be annoying.
Let’s Go On a Date Matoi
Let’s Go On a Date Kirito

Someone’s gay! Is it you?
Well, one of the answers always will be gay because if you’re female, then Matoi’s gay and if you’re male you’re asking out gaily Kirito. If you say Let’s Go On A Date Matoi? She yells and says it’s a very delicate matter! Wait wait later lets discuss it later ok. Asuna says she’s now hit the touchy subject so do your best Matoi. Matoi insists we’re just partners, jeez this is embarrassing. Kirito cuts into the conversation saying anyway since we lost here is your reward. Matoi is excited to see what it would be, and he says it’s the moves they’ve learned-- they’ll teach them. Like a photon art? He says instead, it’s more like a martial arts demo. We tried testing them out but even with the right movements the enemies didn’t take damage.
Matoi doesn’t understand what it means but promises to do her best to memorize it. (This is likely something from SAO show where you have to do 'moves' to activate damage against enemies, preferbly 'in sync' with other people to up the damage.) It shows a cut scene of him doing what looks like PA dance with his dual swords. Then it shows her flying around doing pink zaps with her saber on a gray background. He says his is Starburst Stream and her’s is Mother’s Rosario. You 2 should have no trouble repeating it. You receive the item 670 Sword Skill. Asuna explains that Mother’s Rosario has a lot of precious memories attached so take good care of it. Matoi will cherish it.

Kirito says they owe you 2 a lot so he wanted to talk about something. He’s already said, but brings up again that they’re from a completely different world than Oracle. We can’t get into the details of how we got here (because the morons that made up ‘episode dumbass earth’ of course) Matoi says it’s no problem because they are aware of other dimensions. He says you 2 must have had similar exp’s to their own. (Well not really if it’s the animuuu) He’s been to many worlds in the past and is currently making one called ALO. But, he’s wanted to try his swordsmanship on other kinds of worlds. He could grow as a warrior that way. Matoi asks why but he says that’s a long story…he’s keep encountering situations that lead him to that conclusion. He seems sad, so she encourages him.
He looked into several VRMMOs –he means different worlds and he found Oracle that way. It caught his attention so jumped in. His original plan was to look around a little and leave if it wasn’t a good fit. She joined him because it looked interesting. He wasn’t thrilled when she wanted to come though…But you’re glad she did tho! He agrees and thanks to that they’ve learned and met you and Matoi. Even though you were busy, you guided us. But, we’ve got to go back. People will be sick of waiting for them. Matoi looks sad, and says will you ever come back? Asuna says of course, and we’ll bring our other friends too, we can’t wait to introduce everyone. They hit their logout key and vanish. Matoi feels they were strange but glad they were so nice, she hopes to see them soon.

Xiera cuts in and says oh looks like they left. She finished her investigation so come to the bridge. You do/instantly go there because it is a scene. On the bridge…she says sorry for your day off. Matoi tells her to don’t worry because they were nice and meeting them was lots of fun. Xiera has contacted Enga He couldn’t find their record of access of Oracle on earth. There is no game on Earth called ALO or SAO. So then, could they be from even another dimension? They seemed very careful to point out they were from another world. Xiera thinks it’s a half truth. She had 72 calculations and it’s another Dimension Earth, not the Enga one. (So, all that Mother BS didn't happen for them) A different one with the same name? Paralel universes and dimensions but in short…there’s other places almost exactly like ours but slightly different. In actuality in the past where arks got lost in unknown dimensions after issues during teleportation. (She means the Darker Dimension that you randomly can get into during an attempted TACO run) The causes are unknown but something resulted in interference between the SEED in their earth and ESCA in ours. Resulting in the link that allowed them to log into Oracle like pso2. And their avatars became phantoms embodied from memories and feelings. Her theory is that their bodies are playing the game while they operate the avatars in Oracle. So, they thought they were plugging their brains into another game---actually did, and then that spawned phantoms here which are what you see. THAT explanation makes actual sense unlike the non-explanation for stupidearth. Matoi mentions their outfits were from a world of the past rather than the one they were just at.

They Were Pretty Strange Themselves
I Wonder If Something Happened in That World

Remarking on them being strange doesn’t help anything so if you Wonder, Matoi won’t know what may have happened to them, but those clothes must hold unforgettable memories. Xiera says miracles don’t last forever, now they’re in their own world so they likely won’t be able to reach ours again. Matoi is upset by this, we won’t ever see them again? After all the time we spent, we promised to meet again. A message from Asuna comes in for Matoi. Asuna says she’s glad it got through, so Kirito…He can’t accept their loss after all, at the Harkotan Successive Training. Let’s go 1 more match! Revenge before going back! He’ll be at the same spot, he’s come up with a secret plan to win. Asuna explains he doesn’t handle losing well, if he’d try again, she wants to try the food again so let’s go to Franka’s Café. Matoi cheers she’ll be able to see them again. Xiera reminds her they may have to part eventually but until then, enjoy your time to the fullest. Matoi says let’s go, and it returns you to the upper lobby.

Now, you can turn in the quest.  She’ll say she didn’t expect to win, but is still disappointed. Krito wants to do something else, so challenge us again at any time. This gives her yet another CO, which is

Kirito vs the Guardian
With this, you have to clear any free exploration or ARKS quest with Kirito Asuna and Matoi at A rank or better. For this, any ‘ecological survey’ always works because simply by completing them you always get the S rank because it is enemy point based only. When you go to turn this one in with Asuna, Kirito will ask how we did this time, we must have beaten more of them, right? But, alas, Matoi and Asuna were keeping count and it is a draw. Matoi was surprised but it proves the 2 groups were in sync. Kirito feels a draw isn’t good enough, he wants a rematch.   

This completes all their orders/their plot line crossing over into the game.
So, this was a large event, but it was good to have reiterated how different dimensions work & to have the whole Darker Dimension brought up again because it is so extremely rare to get it (especially in the times this event happened, with players hardly ever running the TACOs (Time Attack Client Orders) to get the 'accident' to happen that results in the DD quest instead. What's hilarious is that the SAO explanation that "you plug your brain into the game" and then the game is like a lucid dream where your body is just laying there / so it is 100% real to you is like a million percent better than the one pso2 actually had. Then, combining it with Phantoms which are the MOTHER/ESCA stuff that's like photons but not & can be used to manifest into avatars is better as well because at least that's plausible excuse in-universe for having Asuna & Kirito there. And all for a mini-side-story crossover that was somehow able to do a better job at plotting than the actual PSO2 game did in that Episode Earth.