How about the very first chapter, when you get A Taste of Power and get to use the summoned eidolon Odin against the Dainsleif? Destroying the soldiers with ease and then one-shotting the boss (well, at least the first stage) with the Zantetsuken ability starts the game with quite a bang.
The Battle of Judecca in Chapter 5, you take some time out from the attack to aid other cadets in danger. Cue repeated Big Damn Heroes moments as Class Zero saves their classmates while a Theme Music Power-Up of the main theme plays.
The climax of the Battle of Judecca. You take command of Bahamut ZERO to fight Shinryu Celestia. Yes, a battle between Bahamut and Shinryu at last. And as your Finishing Move, you charge up Tera Flare, which in this game manifests as Bahamut ZERO calling upon a whole thunder of Bahamut dragons to bombard Shinryu Celestia with Mega Flares. The attack does repeated hits of 9999, so many that the damage continues to pop up and display even as the Five-Star Dragon collapses and slides off the frozen cloud and down into the Strait of Judecca. Even better in the HD remake, where the Mega Flares break the damage limit, doing 18,000-ish damage over and over.
In order to most awesome:
Doing the Bahamut ZERO Vs Shinryu Celestia battle the proper way: spamming Grand Buster while enduring fireballs and thunder blasts, then landing a Breaksight and wrestling her onto the frozen cloud before charging up the aforementioned Tera Flare.
Charging up Tera Flare without the Breaksight stun, which leaves Celestia helplessly trying to blast the aforementioned thunder of Bahamut dragons before they bombard hernote as well as preventing Moglin from telling you to charge up Tera Flare, which just plain doesn't make sense after he's amazed at this epic Bahamut out of nowhere..
Taking down Shinryu Celestia without Bahamut ZERO, by means of constant evasion and several dozen if not several hundred Breaksight hits, which will also land you an S-rank and alternate prizes.
Qun'mi, the White Tiger Secundus l'Cie, deserves mention here. The Rubicus reveals that she was part of the reason the Ultima Bomb was powerful enough to eliminate Lorica in its entirety - she was there, in person, during the detonation. You find the l'Cie Qun'mi's stone at the edge of the blast site - and Orience l'Cie go into crystal stasis if they die, as well as after completing their focus. Negated Moment of Awesome? Nope. Machina took her place as a White Tiger l'Cie by receiving her Focus and mask directly from her - she was fused to the rock at the edge of the blast site. That's not even the best part. The Akademia Liberation - immediately after which the Ultima Bomb was dropped - takes place on Aquamens XII (equivalent to February 12). Escaping the Imperial Capital - after which Class Zero gets to Old Lorica - takes place on Glacemens XXVIII (equivalent to June 28). This means that Qun'mi survived the edge of a blast from a WMD and four months with no food or water, without succumbing to crystal stasis. Demigod or not, that's impressive.
The Final Boss battle is impossible to lose, but contrary to some other instances of Zero-Effort Boss in the series, it still manages to be epic. Empowered by the spirits of Rem and Machina, Class Zero completely No Sells all of Cid's 9999-damage attacks and absorb the Phantoma empowering him one at a time, sacrificing themselves in sequence to slowly but surely bring him down. All while a Theme Music Power-Up of the game's main theme plays courtesy of a Boss Remix.
Clemente getting her revenge on the King of Concordia for the Queen's murder... By just standing aside and doing nothing when the greedy King tries to gain even more power for himself, which results in him being eaten alive by dracobaltians because the object he touches is cursed.
The prologue of the game. Milites has set up a crystal jammer which prevents magic use and is mowing down cadets left and right. Then Class Zero appears...
Some mention should go to the Akademia cadets. If it hadn't been for the crystal jammer stopping them from using magic and summons, they could have beaten the Militesi army without Class Zero.
The Code Crimson mission for Chapter 8, Machina's Struggle has Machina, as the l'Cie Incognitus, mowing down Akademeians left and right. Yes, you probably feel like a right ass for it, but come on, you're hitting the damage cap and one-shotting Golem-classEidolons. Plus, by now you'll likely have his Dark Side ability, which is horrendously appropriate due to being a shot of darkness that hits everything. It doesn't stop there, either. Gilgamesh demands a fight when you get to your destination, and Machina - a Secundus l'Cie of a controlled Crystal - can't even scratch the Focus-forgottenPrimus l'CieKing of Lorica without a Breaksight, even if you're 9 levels up on the mission level. That's right, late-game A Taste of Powerwithout an Anti-Climax Boss.
Mutsuki, who is 15 years old, knows how to set up a bomb in a way that the blast only goes inwards and does not damage surrounding buildings.
In Chapter Four, you have the option to invade the Frosti base in Milites. If you choose to do so, your boss battle will carry on as you fight a machine whilst a sniper takes aim at you. After this, you will take control of Trey, who will proceed to shoot the sniper through the head with an arrow - from 4000 meters away.
Overlaps with Funny Moments, but in the beginning of Chapter 4, when Class Zero is in the Milites capital during the tripartate peace talks, one of the events has an Imperial soldier named Piett mocking Class Zero for being what he considers lapdogs to the Vermillion Bird Crystal, angering Nine, who is about to fight him until King stops him and starts counter-mocking Piett for being a lapdog to Cid, which succeeds in pissing Piett off even more than he pissed off Nine.