There's Vivi's complete and total humbling of the Black Waltz during the airship chase scene, for starters...
Not to mention that, throughout all this chaos, Garnet is piloting the clunky cargo ship through the South Gate as it closes. For a naive princess with a serious lack of world experience, she does a really outstanding job at it, too.
To Alexander easily repelling (and ostensibly destroying) the Eidolon of the Dragon King Bahamut...
Complete with Bahamut's "OH CRAP!" moment when he realises he's on the business end of a Holy Judgement.
The Big Damn Heroes moment when Zidane comes literally flying to Garnet's rescue from atop a crumbling castle tower.
Possibly the greatest crowning moment is that Zidane even survives this BSOD as Zidane's mind and SOUL were LITERALLY ripped to pieces by Garland, his sheer willpower and a few sharp but emphatically caring words from his party are the only reason he managed to piece it back together
For this troper in particular, this scene was made even more awesome by the fact that through a miracle of timing, almost every character's Trance triggered during their respective battles. What topped it off though? The fight alone against the Shell Dragon. Zidane gets curbstomped to within an inch of his life, then Dagger appears and heals him to full health. The Dragon makes one more attack... and then Zidane and Dagger both hit Trance at the same time. Cue Grand Lethal, followed by a full-power Bahamut. Badass.
Backing up just a few scenes, before Zidane has his soul sucked out by Garland, he's about ready to destroy all of Terra and says just as much. The Crowning Moment in this scene is his Badass Boast to his creator:
Zidane: I AM the new Angel of Death! YOURS!!!
To the party being swarmed by hundreds upon hundreds of Nova Dragons at the portal between Gaia and Terra, a battle they couldn't possibly have won... until the entire armed forces of the world arrived to hold off the Dragons. It wasn't so much a Moment Of Awesome for a single character as it was for the entire secondary cast of the game.
This is also considering that all the major nations on the Mist Continent (the only continent on the planet to support thriving cities) save for Treno were devastated in the previous disks by invasion or attacks by the Eidolons. Somehow, Lindblum and Alexandria managed to get their shit together fast enough to come to the aid of the heroes.
My sister and I always cheer when it shows the Invincible racing towards the portal while a group of dragons fly straight towards you, and out of nowhere the Red Rose rises from the clouds to protect you. There's something satisfying about seeing that dragon crash straight into the ship and bounce harmlessly off it.
... And, like above, this scene is a reference to Final Fantasy IV , where the exact same thing happened to prevent the Giant of Bab-il wiping all life off the face of the planet.
Garland trumping Kuja's plan to seize Alexander, destroying Alexandria in the process. Seriously, everything about this scene was awesome- the music, the visuals, the dialogue, Kuja's Oh Crap reaction, everything. But even more astounding is the fact this was Garland's first scene!
The conclusion to his second meeting with Zidane. It looks as though it's building up to a one-on-one boss battle, with the villain toying with the hero for a few minutes until he's finally defeated. But no: he just rips Zidane's soul out.
And revealing just how much plot-related stuff he was responsible for during the party's trip through the final dungeon. The fact that he shows up to help Zidane at all is pretty awesome, too; Garland might be dead, his grand plan may be lost and the Terrans he'd hoped to resurrect have been destroyed along with Terra, but Garland sure as hell isn't just going to pass on when the universe is in danger!
Kuja's destruction of Terra.
Blink and you'll miss it, but Zidane hits his all-time highest level of badassery for one beautiful moment during his mad rush to outrun the impending Iifa implosion and save Kuja. One minute he's running hell for leather away from the oncoming killer vines...and then he manages to leap onto one and effortlessly surfs it most of the way down. While smiling. True, he biffs the landing, but for that fleeting instant, Chuck Norris had nothing on Zidane Tribal.
Garnet finally getting her voice back, cutting her hair, and turning to Zidane with a determined smile that shows both him and the player that she's ready to fight again. Helps that it's followed by the most uplifting music ever as you take the Hilda Garde 3 to the skies for the first time.
On a meta level, the Excalibur II Perfect Game challenge (GameFAQs link) is one of the most awesome achievements in gaming. Getting the Excalibur II requires reaching nearly the end of the game in 12 hours. The "Perfect Game challenge" requires fitting everything missable into that time limit — and check out the guide if you want to know just how much that is. In 2011 and 2013, a new missable item and sidequest were pointed out that each require an extra 20 minutes or so, and the PG specialists still managed to fit them in and have time to spare.