Anime

In the Galaxy Angel S OVA, Col. Volcott O. Huey — a usually calm and laid-back commander — is reassigned to watch over the bratty Twin Stars, whom he expresses patience with until they cross the line and make fun of his mustache, causing the old commander to revert to his badass days on the battlefield where he was known as the White Wolf. He proceeds to fly into a rage, doing everything from repelling gunfire with a kick to growing into a giant and ultimately beating everyone up that he comes across so thoroughly that they turn into statues referred to as "Loser Stones." Rank Scales with Asskicking, at least when you diss the mustache.
Ranpha easily defeating every other contestant in an open wrestling tournament.
Forte versus the literal whale-sized fish monster. First she holds its jaws open as it tries to swallow her whole, then she flips it into the air. Even her teammates are amazed.

Gameverse

Any time they use the Chrono Break Cannon, ever. Even if it was deflected in Moonlit Lovers.
Every single final battle in all six games has the game's opening song as the battle track, usually an energetic and passionate love song that still somehow REALLY fits a raging battle in space with explosions going off everywhere.

During Chapter 8, appropriately named Dark Despair, Tact gives the Angel Tai a Rousing Speech which allows the girls to bypass the Angel Frame's Power Limiter, resulting in a pair of feathery white wings.
Tact's chosen girlfriend gets one when the Elsior gets damaged after the final player battle. Depending on who Tact's girlfriend is, the Angel will either single-handedly clear out all the enemies surrounding the Elsior (Ranpha, Mint, or Forte), recharge the Elsior's power systems by spending all her luck (Milfeulle), or heal the Elsior (Vanilla).
The last battle itself is a CMOA. The battle starts with an eerie silence, no one talks in the radio and no music plays, until the first attack lands on an enemy and Eternal Love ~Hikari no Tenshi Yori~ starts playing.

Before the final battle, Tact's conversation with Nefuria, when the latter mocks them for their "new toy" (Unit #7 attached to the Elsior). Tact replies that it's not a toy: it represents their hope, and how they're going to fight for their future instead of submitting to the Val-Fasq. Nefuria is visibly rattled, saying that she doesn't like Tact's eyes, the eyes of someone who'll never submit. Tact of course takes pleasure in it.
The finale, full stop. Once the Elsior gets in range to launch Unit #7, the rest of the Angel Wing immediately take positions to clear the path from any enemies trying to get in their way. With their help, Tact and his chosen Angel get close to the O-Gaub, activate the Field Canceller to bring down its shield, barely giving Nefuria time to have a This Cannot Be! moment before they fire the Chrono Break Cannon at point-blank range. The supercarrier then goes off a single shot.

Tact's chosen Angel gets a final moment of awesome at the end. Gern had another Chrono Quake Bomb, and it's still going to activate even though Gern has been killed. So Tact's Angel, with Tact in the Emblem Frame by her side, uses the Emblem Frame's wings to suppress a potentially galaxy-wide Dark-Age-causing explosion and live to tell about it! Sure she gets blasted into Another Space for her trouble, but they end up returning to normal space, which is more than the Angel was expecting since there was a real risk she might be killed.
A bit of a Tear Jerker example on this one. Hiromi Sato sang the opening, Angelic Symphony, for the original PC release and was called back to sing a new ending song for the PlayStation 2 release. According to an interview, she cried after recording the new ending, Never-Ending Prelude.