To the point where it's ended up on the same level as Guile's Theme, Guren no Yumiya. Pretty much unarguably agreed upon to be one of the most epic songs in existance. And that isn't even the full version.
Anytime the anime decides to show off the 3D Maneuver Gear in full use, you can expect it to be ridiculously awesome.
Every single time a Titan falls. It is glorious to see those assholes lose.
Every single time Eren opens his mouth. Every single time. Everysingleheroicspeechtropeunderthesun gets used to its fullest. Even when he was nine years old and busy being strangled to death, he essentially turned Mikasa into a superhero just by speechifying to her. Not even Captain America is as constantly inspirational as Eren. Even when he fails, every word out of his mouth is awesome.
Even when he's not speaking, even when He's in his Titan form and just roaring, Mikasa still describes him as the physical manifestation of humanity's anger.
Incidentally, when he was nine, he killed two grown men, hardened killers, with nothing more than a Wounded Gazelle Gambit, a knife, and a kitchen knife tied to a broom. The second one had an axe. It didn't help.
Dot Pixis might as well be a walking one, purely because in a world full of meaningless violence and wasted deaths, when things are making less and less sense every day, he never loses his cool and never lets the (increasingly horrifying) circumstances cloud his judgment.
It's a villainous one, but the first appearance of the Armored Titan in the anime is simply beyond epic Especially considering how brief this scene is in the manga where it's mostly off-screen, and only a handful of panels at best.
Sasha showing lightning quick thinking and reflexes to save Samuel from falling to his death. It's one of the first real indications that she's more than just a ditzyfood-junkie.
When Mikasa initiates the first death of a Titan in the series. She kills four total without breaking a sweat. The only other people with a higher Titan kill count than her are Eren in his Titan Form and Reiner. That makes her a One-Woman Army, acknowledged In-Universe.
After this, her "The Reason You Suck" Speech to the guy who was blocking the gates with his merchandise because he thought it was more important than the lives of any of the people trying to get through.
Mikasa: Right now, my comrades are dying. Because the people haven't evacuated, they're dying, fighting the Titans.
Entitled Bastard: Of course! It's your job to sacrifice yourselves to protect the people's lives and fortunes! You parasites think you're so special just because you're finally being useful for the first time in a century!
Mikasa: (Death Glare and Slow Walk commence) If you expect someone to die for the sake of another as a matter of course, I'm sure you'll understand this. That sometimes, a single noble sacrifice can save many lives.
Entitled Bastard: Try it! I've known your boss for a long time... I can decide your fate with a single word!
Mikasa: (casually knocks out all of his bodyguards) How is a corpse going to talk?
The defeat of the Titans in the supply warehouse. The human side does not suffer any casualties.
Even better when you realize that Mikasa unknowingly avenges Mina's death when she kills the same Titan who ate Mina earlier.
When one particular Titan begins killing other Titans. Doubly so when it is revealed that it was the previously thought deceased Eren who comes out of its disintegrating body, revealing he did all of that.
That moment of sublime badassness when the Rogue Titan punches some other Titan's head ACROSS THE TOWN. The closeup of its stupid face embedded in the window of some building is the icing on the cake.
Said moment comes right after Mikasa's despair over Eren's apparent death causes her to crash. Two Titans close in on her, and she is on the verge of giving up. Then she remembers Eren telling her to fight, and with tears in her eyes she vows to somehow live on. From what we had seen up to that point, the viewer could be forgiven for thinking she would die. Then we get this.
In episode 8, while making a run for the HQ, Jean gets grabbed mid-air by one of the Titans. With a single swing of his sword, he cuts off one of its fingers and frees himself.
Also in Episode 8: Eren, in his Titan form, is getting weary and the Titans are chowing down on his body faster than it can regenerate... and then the jumping Titan who ate Thomas happens to come by. Eren tears through the Titans holding him back without any arms, and then rips out the nape of its neck with his teeth. Eren had been single-mindedly chasing that exact Titan when his leg was bitten off; he got revenge for Thomas after all.
With episode 9 comes the famous Survey Corps leader, Levi. His first moment in action has him mowing through two huge Titans with effort comparable to swatting a fly. He even audaciously stands on one's head and casually reloads while it wails in pain due to having a pair of three-foot-long blades jammed in its eye sockets.
After finally realizing he's not the burden to his friends he thought he was, Armin gets a serious confidence boost and marches straight out of the smokescreen to confront the Garrison troops that were threatening them. The guts he showed to not only stand his ground with his argument, while facing certain death of the cannon they got readied mind you, is truly something to behold. And this is just the start of the amazing character development he receives.
Mikasa's Badass Boast in the scene before Armin takes over arguing their case, where she reminds the Garrison at large that she's spent the last couple years honing the skills to carve up flesh with absurdly sharp blades, and being damn good at it. And that if they come any closer to Eren they'll get to see her use them.
Morale is low among the soldiers after the Titans assault Trost. Crushed by the fear the Titans instill in them, they attempt to desert their posts in order to spend the little time they have left with their families. So what does Dot Pixis say to convince them to fight?
Dot Pixis: Those of you who would leave their parents, siblings and loved ones to experience such terror for themselves... are all free to walk away!
Jean using the hooks on his 3D Maneuver Gear to stab a Titan that was about to grab Connie in the hand in episode 12, drawing its attention onto him. He claims that the reason he did this is "I've had enough of people dying on my account."
Episode 13 is full of these. First we have Marco, Connie and Annie working together to save Jean.
One last Titan remains in Eren's path, and suddenly Rico comes out of nowhere and stabs its left eye out. Then Mikasa finishes the job.
Eren blocking the gate, giving humanity the first victory over the Titans with "Call your name" playing in the background. "Everybody... didn't die in vain.", indeed.
And finally there is Levi's Big Damn Heroes moment, saving Eren, Mikasa and Armin from two Titans without breaking a sweat.
There is also just something inherently awesome about Eren holding the boulder above his head as he heads towards the gate. Maybe it's the fact that he's holding the boulder up despite the fact that it's twice his size, maybe it's because he's doing something that all of Humanity tried to do and failed, maybe it's the steam billowing around him as he does it, maybe it's the glowing green eyes, maybe it's the music, maybe it's the fact that he bears a striking resemblance to the Greek Titan Atlas, or maybe it's all of the above combined. Whatever the reason, it is simply awesome.
There are a few ones with the fight with the Female Titan in episode 17
Jean, Armin and Reiner attacking it in order to buy time for the main formation to retreat, despite all evidence pointing to them being severely outmatched.
Armin figuring out about the Titan looking for Eren and screams to Jean about avenging his death, causing the Female Titan to hesitate when it was about to kill Jean.
Reiner managing to cut his way free of the Female Titan's hand. This is after it looks like he's completely done for after she pops him like a grape; after escaping he's still healthy enough to walk it off and carry a shocked Armin with him like a sack of potatoes. Although this is significantly less awesome if you're up to date on the manga.
Eren's fight against the Female Titan in the forest. It's a mainly even fight, until she lands a pretty good punch in his face... which he uses by sliding his teeth alongside her arm and punching her a good few metres up in the air. Unfortunately he gets distracted as he realized the Titan was Annie, allowing the Female Titan to beat him.
Levi blocks a punch from the Female Titan with his foot. And using the momentum he got from the attack to rescue Eren.
Mikasa watching in awe as Levi sliced up the Female Titan, commenting that he moved too fast before the Titan can defend herself.
Episode 24/25; Chapter 33: The final fight with Annie has:
The moment Eren finally gains the resolve to fight and possibly kill Annie the Female Titan he's already been Impaled with Extreme Prejudice and crushed by debris. It doesn't stop him at all.
The Female Titan, using a sweep kick that cuts Eren's leg off
Which doesn't slow down Eren, he just jumps using his remaining leg and punches the Female Titan a few meters back.
As the Female Titan counterattacks, Eren catches the attack using his mouth. AGAIN.
After the Female Titan has pretty much knocked out Eren and is heading for the walls, Eren comes leaping out of the crater of a building he's in, on fucking fire and hauls ass towards the Female Titan (let's note he's missing an arm and a leg at this point) and slams her into the ground. When she covers her neck, he decides that the obvious answer to this is to tear off her face. The Female Titan freaks out completely and tries to climb the wall, even severing her own leg to get away from the demon she's fighting. Then Mikasa cuts her fingers, and Eren decides it's lunch time. Of course, this is only the anime version. In the manga version...
...the Female Titan is defeated by a combination of Eren, Mikasa and Armin working together. Eren launches Mikasa to catch the running Titan, allowing Mikasa to cut the Titan's fingers off and kick her down the wall. All thought up by Armin.
Chapter 36. After a surprise attack catches her without her gear, Sasha takes on a Titan with a bow and arrows in order to buy time for a child to escape. After shooting one of the Titan's eyes out, she jumps at him with the last remaining arrow and stabs his other eye out, allowing both her and the child to survive.
Chapter 39: Where do I begin? Bertolt stabs a Titan in the eyes with a pitch-fork; Connie, Ymir and Krista immobilize the same Titan by rolling a cannon down at it from on top of the stairs; and Reiner saves Connie from another Titan by blocking its bite with his arm, putting it over his shoulder in a fireman carry, and was planning to pitch it out a window along with himself. Thankfully, Connie cut the Titan's jaw and freeing Reiner's arm, and Ymir boots it in the face while Bertolt also pushes it out the window.
Chapter 42: Bertolt turns into a Colossal Titan and attempts to make off with Eren. Mikasa ain't having any of it! Without hesitation, she leaps at the opportunity to take on the monster essentially responsible for most of the suffering she's gone through in life. Mikasa in general should get a special mention. She easily could have been nothing more than a Faux Action Girl and cheerleader for Eren, as is commonplace for girls in this genre, but instead we get a hardened BAMF who cares deeply for Eren and will defend him with her life, even when Eren had just emerged from the body of a Titan and her superiors were getting ready to murder him.
Chapter 44: Eren shows us why he deserves the title of Humanity's greatest hope. When he fights the Armored Titan Reiner, he uses all the moves that Annie taught him and even lampshades how much of a blunder it turned out to be, giving him the advantage. Remember, this is the Titan that could easily destroy walls by himself. Near the end of the fight, Eren has the Titan pinned and is about to rip off its neck until the Colossal Titan jumps on both of them.
Hannes gets a surprisingly subtle one after Eren is kidnapped. Not only does he prove that he's not the useless, drunken layabout he was five years ago, but he also makes it very clear that, even with all that's happened, he understands the bond between Eren, Armin, and Mikasa, probably even better than they do themselves. Doubles as a Crowning Moment of Heartwarming; he's been watching over Carla's kids long after he rescued them.
Chapter 49 should be called "Erwin Smith is a Badass". When caught by a Titan, he screams for the others to continue the mission. Later on, he shows up missing one arm and rescues Eren before leading the retreat.
Then there is Krista saving Ymir, killing her first Titan in the process.
And the real crowner is Armin showing off some impressiveManipulative Bastard cred to get Bertolt to lose his cool and allow Erwin to make his move to cut Eren loose.
Chapter 50, we finally see why everyone is after Eren so much.
After a heartwarming speech from Mikasa, Eren gets his heroic will back, and punches the Smiling Titan, the one responsible for eating his mom and who has just eaten Hannes as well, in his human form. It goes about as well as expected. But Eren doesn't give up and from his back a Titan roars and attacks the Smiling Titan. And is followed by every normal Titan around them. Revealing Eren has the ability to CONTROL ALL NORMAL TITANS. Eren takes this chance to escape, when Reiner approaches, Eren threatens him and commands the Titans to attack Reiner, stopping them from following and letting everyone get away.
Krista boldly correcting Connie about her name and then tearing Ymir a new one for lying to her once again. Followed up immediately by declaring that from now on, they should live for themselves only and that she will never fear anything as long as they can be together. Cue them charging into battle together with renewed determination, and kicking ass along with Connie.
For Character Development. What does Armin do the first time he's faced with a Titan eating one of his friends right in front of him? Absolutely nothing. He's too afraid to move, and Eren gets eaten. What does he do the next time this happens, in Chapter 50? Drags Jean, who's unconscious, away from an advancing Titan with one arm, then manages to get him onto a horse so they can escape. He's still got maneuver gear and even a little bit of tree cover, but he stays on the ground, the single worst place to face a Titan, to protect Jean until Eren's new powers open an escape route. Holy cow, did Armin take a level in badass.
Chapter 52: Pastor Nick endured brutaltorture and still refused to give up his secrets, taking them to the grave. Dude's got balls.
Also in chapter 52, although it's a minor example, when some Military Police members start physically and verbally harassing Hange when she questions them about Pastor Nick's death, Moblit grabs one of them by the wrists with a seething glare and very firmly states their positions in a way that just screams for them to try to disrespect her again.
Chapter 54 is just one massive moment of this. Mikasa and Levi effortlessly subdue the kidnappers who abducted Armin and Jean disguised as Historia and Eren respectively without even giving them a chance to fight back. Keeping the awesome coming, Levi browbeats the leader of the abductors (who turns out to be the Jerkass merchant who blocked the escape tunnel in the battle of Trost) into telling them what he knows, blatantly dismissing his fears for his and his men's lives. However it is the way Levi does this that is the most amazing; he compares the situation to the risks the Survey Corps take fighting Titans in a way that can't be called sympathetic yet is at shows he understands what the leader is going through. This results in the capture of a high-ranking member of the Secret Police and perhaps the first answers on what the hell is going on with the Government Conspiracy.
Also Sasha showing off her Improbable Aiming Skills by destroying an extremely tiny pistol the leader of the kidnappers pulled on Mikasa in desperation, her only response to Jean's furious protest that Mikasa could have been injured being, "She shouldn't have taken her eyes off the prey". Way to go Potato Girl!
Related examples outside the series
There is a very well-made Attack on Titan tribute game, made with the Unity engine, that can be found and played here. What makes this a CMOA is that this whole thing is made and maintained by one guy; Chinese developer Fenglee.
CryziesX is one of the most badass AOT players on Youtube. His skills with Levi do the original serious justice and must be seen to be believed.
Another one for Fenglee, managing to add a boss level for the Female Titan into the game in the most recent update. It is markedly different from the majority of the game, as normally, your are stuck in the village while it is overrun with Titans. Whereas in the boss level, you are in the forest where everyone goes to try and capture the Female Titan. You have trees to use as vantage points (so can she), and she needs a whopping 1000 health taken away from her neck to be taken down, and her ankles (which you can hit to get her on her knees and make her defenseless) can take even more. She is also constantly using martial arts, which gives her sweeping kicks and scythe hands, so it make the whole thing that much harder. And after she is killed, the whole area gets ''filled with Titans."
Another Node example relating to the above: Throughout most of this video, the LAN Party are constantly dying against the Female Titan, including one memorable instance of Sam as Eren trying to take her on in Titan mode and getting utterly massacred. But, at the 24th attempt, after everyone else has died, Niko (skip to 9:24) manages to kill the Female Titan on his own, and takes down 2 more Titans before he is bitten and dies.
The awesome continues as Fenglee adds The Colossal Titan mode, allowing you to take down the gigantic bastard as you defend the city.
And now the recovery of Trost where the players have to defend the AI-controlled Titan Eren as he carries the boulder through the city to block the breach.