Bart got his moment to shine in his A Day in the Limelight episode when he singlehandedly destroyed a harvest ship.
Hibiki has plenty of these, but when he says Dita's name just before the end credits in the final episode, he manage to top everything else he did during the entire series.
Paksisis the thing that obliterated a superweapon about to blow up the galaxy, when everyone else was powerless to stop it, just because it wanted to protect its friends.
In the first season finale, Hibiki and Dita flying out of a solar flare and punching through the enemy flagship after it survived a direct hit from another solar flare. It can also be argued that the whole collapsing a gas giant in order to create a star to blow up the enemy fleet with qualifies as a Crowning Moment of Awesome for everyone involved.
The first time that the four main characters form to make Vandread Pyoro.
The four main characters response to an attempted Breaking Speech in the series finale.
Pyoro gets one. In episode 2 of Second Stage, right after the power is restored to the whole ship and the elevator was plunging, Pyoro blocked the elevator from falling entirely by itself!
Bart gets one in episode 3 of second stage. Also counts as Took a Level in Badass. When protecting a pretty much diseased planet, where he got attached to a permanently sick girl, he unleashes Nirvanas secret weapons.
How about the final episode Just about everyone that the cast has met is now grouping together to defeat the Harvesters up to and including The Navies of Tarak and Majale defecting en masse.
The first time we see Vandread Dita, the rips open an opposing ship with its bear hands before obliterating it.
Super Vandread's debut, in which it effortless stomps a fake Nirvana robot hundreds of times its size.