Just about the entirety of Chapter 1 is a few hours long Moment of Awesome in itself. The party including Hope and Comic Relief character Sazh defeats giant robots, dozens of soldiers and mechanized monsters, and fights a fal'Cie and mortally wounds it, and they hadn't even become l'Cie yet!
Moms are tough. Hope's mom saved Snow from a gunship by firing a rocket launcherup its laser's ass.
Lightning planning to let Hope survive at the expense of her life, then the instant Snow's started his attack, instead of just standing there, she dashes right into battle and kicks ass until Snow's done.
When the party first goes to Gran Pulse. l'Cie also appear to be expert acrobats.
The one scene with Sazh and Vanille, the two comic relief characters escaping from the Palamecia. Both of them are being held hostage, but when two guards come in to take them away, one is taken out by Sazh after his chocobo chick body slams his face, and when the automated flying thing tries to apprehend them, Vanille picks up a gun, screaming as she empties a clip into it. In FFXIII, you don't mess with the comic relief.
The scene shortly before their capture where Sazh just found out Vanille's secrets and nearly shoots her, than nearly shoots himself is a more meta CMOA for Vanille's (English) voice actress, culminated in this one scene:
Vanille:"My name is Oerba Dia Vanille. I'm a l'Cie from Gran Pulse—and to everyone on Cocoon, evil. Shoot me! For your son."
It's also a crowning moment for the characters themselves. These lines may not seem impressive, but in context, they rival Assault On Eden in terms of awesomeness.
Vanille:(broken voice) "It's not over..." Sazh:(fires over Vanille's shoulder) "Okay, fine! You want me? Come and get me!"
Lightning on the Purge train at the beginning of Chapter 1. The train hits a bump in the tracks, and without a weapon, she bashes the guard and then takes over the train.
Shortly after that, she becomes one of the only Final Fantasy characters to do what any sensible person would do when surrounded by modern military tech. Pick up a fucking rocket launcher and start blasting things!
The beginning of Chapter 12, where the party begins their Assault on Eden - just all of it.
In the second cutscene of Chapter 12, when Lightning leads everyone in jumping off of the Grand Prix track. She falls maybe 500 feet, makes the landing, and kills about a dozen Homeguard and PSICOM soldiers before Vanille lands.
Lightning's has a series of them in the first half of the game. She blows up trains, armies, aircrafts, zombies, and a god like being with a casual self-assurance that makes her act like she's just going to pick up some bread from the store.
Lightning shouting "I'm No One's Slave!" when she uses Army of One in the final battles of the game, especially against the final boss' first form.
Army of One alone is awesome. Push an entire group of enemies into Stagger and watch as the percentage easily skyrockets to 999%.
Hope, in Chapter 7. He tries to fight the Ushmajal Subjugator by himself, after Snow gets swatted aside.
Hope: "Always the hero. You want to die? ...You can't."
"Battle Team Changed—Hope: Ravager"
Hope: "I won't let you!"
Even the interface gets a CMOA here.
Just when it looks like Hope's toast, Lightning and Fang come out of nowhere and have their own Big Damn Heroes moment. Suddenly a Hopeless Boss Fight becomes a No-Holds-Barred Beatdown.note With careful management of the Paradigms Hope could kill the thing by Cherry Tapping it to death all by himself. It'd still be easier to take a pounding to bring Lightning and Fang in though...
Hope gets another one just before the final battle:
Hope: "You say you want your Day of Wrath, do you? Well it's coming right up!"
Snow has a lesser Big Damn Heroes moment in the very first chapter: Hey C'ieth, you want to chunk up Tagalong Kid Vanille and Hope? Not if Snow's fist has anything to say about it.
Dysley gets one when the heroes first confront him. Seeing a frail old man effortlessly destroy numerous troops, including Jihl, is quite a sight. Then he follows it up with an epic speech to open the fight:
Dysley: "I am fal'Cie. My name is Barthandelus. Voice of the Sanctum and Lord Sovereign of the Cocoon fal'Cie. Your kind feared the dark and so we gave you light. You begged us for the Purge and did it not come to pass? Now you spurn our counsel? You must learn your place!"
Vile Peaks with Hope in a Mini-Mecha. The only downfall of that Mini-Game was that it was too short.
Hope is an instant away from killing Snow. Then there's an explosion, and Hope gets knocked off the side of the building. What's Snow's response? Without even thinking about it, he drops off the side of the building, grabs Hope, and cradles his body with his own to shield him as they fall through multiple panes of glass and hit the ground.That is what it means to be a hero: to save the ones who want to kill you. Then, when Snow recovers, despite being so badly wounded he can barely walk, he puts Hope on his shoulders, pockets Hope's knife, and then proceeds to haul him across the city. That is where Snow went from a well-intentioned idiot to a true hero worthy of the title. See the whole scene here.
He's shown at one point to be scaling a building rung by rung. Despite being badly wounded and carrying Hope on his shoulder, this guy will NOT GIVE UP.
The gang is surrounded by a squadron and battleship bent on killing them. What does hotheaded Snow do? He comes out peacefully and tries to reason with them. From the way things were going before Yaag stepped in, it was working! Take a moment to realize how much sheer charisma it'd take to get over that kind of paranoia and hate.
What about right before this? Hope gives Snow a reason you suck speech that's pretty much the first thing to crack Snow's idiot hero personality. Then Hope blasts Snow off a ledge and nearly stabs him while he hangs helplessly. In other words, your WhiteMage nearly one shots your StoneWall, both physically and mentally.
A truly underrated example in Chapter 10: As you waltz through the Fifth Ark, you come across Cid Raines. Shortly afterward, Lightning assumes he's a traitor and attacks him. By this point, Lightning has proved herself as a very capable Action Girl but when she attacks Cid Raines, he stops her strikes barehanded (he has gloves, but still), briefly takes her gunblade, and sent her flying. In other words... he just curbstompedLightning.
In addition, the revelation that he's a l'Cie, and the immediate boss fight, show that Cid Raines is truly an underrated character.
In this scene after finally killing Barthandelus, the party looks on in awe as he melts away into the abyss. Everyone except Sazh, that is. He has one thing to say:
Fang: He's a biogenitor - chews up one species and spits out another.
Despite the above, the Adamantoises themselves. XIII set one heck of a trend for these monsters, turning them into utterly titanic battles. Their tusks and jaws along are larger than a full-grown man.
After spending ages dodging Behemoth Kings, one jumps you, and you find out that you have levelled up enough to take one out without any help from Pre-emptive Strike or Mêlée à Trois.
The Zenobia hunt. A vicious-looking Cie'th with writhing tentacles for fingers emerges from the ground and prepares to do battle with the party...and then off-screen, a Tonberry rushes in at high speed, and kills the Cie'th in one hit with its knife. The subsequent battle subsequently confirms that Tonberries have taken significant levels in badass, going from a Mighty Glacier to a Lightning Bruiser.
The Attacus hunt, though sadly there's no fake-out like the above example. Titan drops a Behemoth King for the party to fight...and then on a nearby cliffside, Attacus himself appears, reverse-wielding a katana that would make Sephiroth proud and Gilgamesh flush with desire, before leaping off the cliff, slicing the Behemoth King a few times, and then by means of Offhand Backhand impaling the Behemoth King and throwing it off the cliff before taking on the party.
A post-humous one for the unnamed l'Cie who narrated Mission 64, the final mission against the Secret Boss, Vercingetorix. The main characters fight this as THE last challenge of the entire game. The unnamed l'Cie defeated it single-handedly.