Kaga and a dozen Ring of Gaea members get one during the fight with Xi Wangmu. After she shows herself to be practically invulnerable, several fighters, including Kaga, swarm her and get devoured. However, they continue to fight from inside Xi Wangmu's innards, weakening her to the point where your party can kill her. Sadly, they still perish, but it's still incredibly impressive.
Going the Law path at least once is worth it because you can fight Mastema again. Then again, this version of him is far from the Jerk Ass he was in Strange Journey, so...
The Neutral path has Burroughs giving White Issachar an incredibly satisfying Shut Up, Hannibal! speech. In the Law and Chaos paths, it's Jonathan and Walter who call him out on his ludicrous posturing and tell him to shove it, calling him and by extension the White as a group cowards who do nothing more than spout excuses.
Burroughs: Scanning... *Scans White Issachar* Excuses, unjustified resentment, self-justification, a rash desire to negate oneself...I don't see any good reason to join their cause.
Jonathan: A pretty speech, but it sounds to my ears like so much unjustified resentment and self-righteousness. We who fight for the people shall never join you in your cause!
Walter: I'm sorry, but I still hear nothing but excuses from your lips. We're out to strike down the old order of things! How could we find common cause with cowards like you?
Tearing the Ancient of Days apart, crushing Sanat beneath your heel... and realize life is returning to Blasted and Infernal Tokyo after all.
The fight against the Ancient of Days particularly stands out. Not only is he incredibly difficult to beat, but defeating him means that you've destroyed an avatar of God.
Completing For the Past... For the Future. You restore the rampaging Masakado and ensure history is put on track as the Firmament forms, earning the game's best demon, many thanks from Masakado himself, Stephen and Burroughs, and saving, quite literally, everything and everyone.
Even if it's brief and conditional on picking the right answer to his taunt, it feels wonderful to hear Merkabah, Knight Templar though he may be, acknowledge you as the Light for the Unclean Ones in opposition to the Light of the Lord. Same goes for when Lucifer, even if just as briefly, recognizes you have what it takes to be the Light of Hope for Tokyo if you answer him correctly. Hell; every time you get the right answer to a boss' taunt and throw back their words at them, or empower yourself with the sheer might of your beliefs, it is indeed a Moment of Awesome.
The DLC Archangel Battles. Yeah, you do fight Merkabah and all, but payback against the self-righteous bastards themselves is so sweet after the pants-wetting they gave you and your friends at the Cocoon. Not to mention they have one of the best boss themes in the game, between the remix of SMT I and II's LAW themes and the "HALLELUJAH! HALLELUJAH!"
Finding a Fiend. David, the Infernal Ikebukuro Horsemen quartet and Mother Harlot don't count. It doesn't matter if you beat them; just finding one of them is an accomplishment in and of itself.
On the same note, the Infernal Ikebukuro Horsemen quartet. No other Megaten game to date has you fight all four Horsemen AT ONCE.
Beating one is a very awesome moment for the player. Think about it: you are fighting a very powerful enemy that always gets the first move, has at least five Press Turns to use, possesses skills that can easily tear through your defenses, are capable of using tactics to find the best way to wipe out your entire party, and more health than the Final Boss of any route. The deck is very much stacked against you...and you won anyways.
Killing the Black Samurai / Yuriko / Lilith, because as Burroughs points out, it completes two quests at the same time. Enjoy the massive dump of EXP.
The Terminal Guardian gets a couple awesome moments as well. For one, it's his sheer determination in not letting you access to the terminals. But specifically the last two fights with him. The fight of which he summons Mara, that while infamous for it's design is still an extremely powerful end-game demon, and the last one which looks like at first a bit of an anticlimax boss being two demons that are not that difficult but he then fuses them to create Shiva, one of the highest level demons in the game.
It's very hard to achieve, but if you can get your entire party to Smirk at the same time, everyone in it gets a full party heal.