Kirito calmly revealing his level to a group of mid-level bandits, and explaining that, even attacking together, they can't overcome his Healing Factor. He then sends every one of them to prison with a teleportation crystal.
Kirito makes losing awesome. Yes, he lost his duel with Heathcliff in Volume One... but Heathcliff had to go all out, and use the system over-assistnote something that allows GMs to counter all Sword Skills, completely disregarding normal system restrictions and limitations to beat him.
One of the best instances is in Volume 7. The Sleeping Knights and Asuna are trying to sortie the level boss, but are being blocked by 20 members of an opposing guild. The Sleeping Knights decide to charge through them, but are about to be overwhelmed: there's only six of them and Asuna. And just as the guild's 30 reinforcements arrive... Kirito pulls a Big Damn HeroesYou Shall Not Pass moment. It should be noted that technically, the only reason Kirito doesn't succeed in soloing 50 high level players is because while he's attacking them from the front, Klein is attacking them from behind, both of them bantering at each other as they take on the guild. By the time the guild defeats them, the Sleeping Knights have won.
In his first duel with Shino, at the end she fires a fifty-cal round at him. Kirito cuts the bullet in half.
Also, going on to be co-winner of the tournament, despite being a novice GGO player.
At the beginning of Fairy Dance arc, in his first fighting appearance with the ALO system, he creates a sonic boom when he starts running. That is how fast he can react when the system doesn't restrict him.
Before that, his display of his sword skills in a real world sparring match, having barely got out of physio and still skinny from the 2-odd years spent trapped in SAO, is arguably more impressive, as he forces his sister/cousin Suguha, a National-level Kendo practicioner, to work hard to beat him. Keep in mind that he was able to read her moves and keep dodging, and she only got her shot in after his exhaustion forced him to slow down and stumble, and when he tried to use a Sword Skill, to obvious effect.
In "Morning Dew Girl", he uses Yui's temporary GM access to hack the system in order to keep her from being deleted.
Also, the end of episode 1 of the anime counts as a CMOA for Kirito, the writer, and the anime team. To be specific, Kirito thinking "I... I... will survive... in this world!" And then shouting at the virtual skies. While one-hit-killing a wolf. With a totally awesome sword skill. Fifteen minutes after learning he's been trapped in a Death Game.
Episode 20. His duel with Eugene, the Salamander general. He holds his own with lower level gear against Eugene's ultra rare sword... And then he borrows Leefa's katana annd goes dual wielding on Eugene. Without Sword Skills.
Episode 23. Kirito's battle inside the World Tree. The first try doubles as a Heartwarming Moment when Kirito has flashes of memories of Asuna as he fights, which makes him more and more determined and fierce. How can anyone NOT cheer him while that happens?!
Kirito is so skilled as a swordsman, he can deflect bullets using the bullet prediction path as a means to guide his sword. In his final showdown with Shinon, he sees her eye through the scope of her sniper rifle and manages to predict where her shot would land and deflect it without being able to use a bullet prediction path.
There also is the point, at the beginning of the Phantom Bullet arc, when he predicts where the bullet prediction beam is going to appear in order to be able to evade in time. It's what defines the reason why he is so good in these games - because unlike other players, he does not limit himself to what the system allows him to do.
When Kirito returns to ALO with abilities from GGO, he is able to easily slice attack spells making him one of the best players of ALO, no ID Heathcliff required.
In the novels, instead of throwing him up and letting him fall onto the sword, he finished with deliberately piercing his eye with the sword. With the pain absorption off.
Which means that he feels the full and real pain of having his eye stabbed (on top of the aforementioned injuries) which continues on as phantom pain in the real world, even if his body is physically unharmed. Ouch.
Just as satisfying is his pwning of Sugou in real life. Sugou attacks him with a knife on his way to the hospital and overpowers him, fortunately his time in SAO and ALO gives him the skill to disarm the bastard, smash his face into a car so hard that it dents then holds the knife to his throat , considering to kill him, cue Sugou passing out from fright. Badass.
Even better? The only reason he survived the first blow? Sugou has no depth perception...BECAUSE HIS RIGHT EYE IS BLIND FROM PURE PAIN!
If you look closely you can see steam rising up from between Sugou's legs after he screams. After spending an entire volume/half season hating him more and more, it's incredibly satisfying to see Sugou so thoroughly humiliated.
Kirito: Such a weak weapon(Sugou's knife). Light. No reach. But it's more than enough to kill you.(cue Oh Crap from Sugou)
In Volume 9, when facing the goblins:
Kirito: “NO! I’M NOT GOING TO TAKE YOU ON! —I’M GOING TO OVERCOME YOU!”
Taking out Kayaba at the end of the Aincrad arc. Also, the way he figured out who he was was just genius.
After the defeat of the floor one boss, Kirito realizes he has to do something to prevent all out discrimination towards the other beta testers. He proceeds to put on a badass Jerkass Façade, stating how he is an entirely different breed of SAO beta tester, gracefully accepting the title Beater and putting on the reward he'd gotten for defeating the boss, a Badass Longcoat, to punctuate his new leagues above status.
In Volume 1 (Episode 10 in the anime), realising that Kirito is in danger, she Flash Steps to him, arriving in the nick of time to save him. In five minutes, she covered a distance that had taken Kirito one hour to travel. She isn't called The Flash for nothing.
Kirito does some ballpark calcs, and realises that Asuna somehow broke the system limits, without conscious effort.
In Volume 2 (Episode 11 in the anime), when she curbstomps a group of arrogant ALF soldiers. Yes, the Truce Zone keeps you from taking a fatal wound inside towns... but the physics engine means that the force from an extremely fast sword repeatedly hitting you in the head will knock you out.
In Volume 7, when she leads the Sleeping Knights in defeating the level boss. She wasn't KoB's subleader just because she was a pretty face.
Kirito and Asuna
Basically, every time Kirito and Asuna fight together, awesomeness ensues! Here the stand out examples:
Right from their first fight together in Episode 2 against the first floor boss. Seeing them coordinating their attacks so perfectly is quite a view. Also, the fact that this is the first action scene in which we listen to the Luminous Sword theme definitely helps.
Even in Episode 12, when both get curbstomped against the unknown enemy! There's something endearing about the way the two of them form that joint defensive stance. Even if said stance doesn't make any practical sense!
And finally, the battle against the Skull Reaper in chapter 13, when Kirito and Asuna show how much they understand each other in battle, fighting practically as one single warrior.
In the climax of the Phantom Bullet arc, Shinon sniping Death Gun's suppressed sniper rifle, destroying it... and she did this without a scope, as her scope had gotten trashed and the Hecate lacks backup iron sights.
Actually, the Death Gun's rifle and Shinon's scope were both destroyed at the same time. Doesn't detract from the awesome though.
A couple from Volume 6 that involve her getting over her fear of guns while in the real world:
Shino is confronted by one of the people behind Death Gun and is about to receive a lethal injection. She manages to turn the situation around, mustering the guts to threaten him with a model gun.
The second is when Shino is confronted by a Girl Posse that regularly bullies her. The leader bought a model gun with her in order to intimidate Shino. When it fails to fire, Shino calmly takes the gun and fires it herself, and calmly walks away, only collapsing when they're out of sight. This is a far cry from when someone merely making a finger gun and a banging noise was enough to make her break down.
In the sidestory "Caliber", Shino uses a special arrow to snag a falling Excalibur. Note that she was firing from an unstable, rapidly descending position, and her bow was only rated for a range of 100 meters, and Excalibur was over 200 meters below and falling rapidly. AND said special arrow has a different handling from normal arrows. And she did this by aiming with the naked eye.
One offscreen: Her very character build. She essentially ignored every other logical option and went straight for the Difficult but Awesome sniper build. She turns every battle against spellcasters a pathetic Curb-Stomp Battle.
His one biggest CMOA was at the end of 4th volume/1st season of ALO. Remember, Kayaba Akihiko? The dude that is already explicitly stated to have died by overloading his own brains with a super powerful electromagnetic brain scan at the same time as the fall of Aincrad?
Kirito, for all his skills and illegal stats was a player was fighting and losing against Suguou/Oberon, the administor of ALO and resident jackass. So, Kirito was near dead and about to get stabbed an Excaliber wielding nut job with his pain limiters turned off. Then Kayaba Akihiko's ghost pulls a Big Damn Heroes moment by giving Kirito admin powers. The moment is handled like the god of world granting divine power to his champion. Kirito then summons Excalibur straight from resident Jerkass's hands.
Earlier, in his guise as Heathcliff, Kayaba duels Kirito. The resulting battle is a thing of awesomeness for both sides.
His in-universe crowning moment of awesome is when he held off the boss of the 50th floor alone for ten minutes.
It's less impressive after we find out that he programmed the game to grant him invincibility when his HP hit 50%+1.
Perhaps the most amazing thing that he ever did comes from a simple realization that Kirito has while fighting him - this is the man who designed the fighting styles of SAO. Every single player's fighting style is based around techniques that Kayaba created.
Kirito's second assault on the World Tree(episode 24 in the anime) is just as awesome, if not more awesome than the first. Only this time he's not alone in the awesomeness.
Upon learning that the guardians target healers, Recon takes it upon himself to drag the aggro away from Lyfa so she can heal Kirito. And when the guardians eventually overwhelm him, he pulls off a Heroic Sacrifice by using dark magic to blow himself up, taking out a large number of guardians.