The moment when it is revealed that the slacker Reaper Koki Kariya is actually one of the most powerful Reapers, and passes up chances to advance in rank simply because he doesn't want a desk job. Even his boss fight is great, since he complains about having to fight the whole time.
Especially awesome if you get the joke of him calling the attack "Level i Flare". In Final Fantasy, Flare is one of the most powerful Black Magic spells; "Level x Flare" targets all enemies with the level divisible by the number given. This results in Minamimoto targeting and blowing up pretty much everything in his combat range.
Level i flare is so immensely powerful because it hits enemies on every plane simultaneously, which is why it was even a threat to Joshua in the first place: he doesn't have all his godlike powers in the RG, so he would have been seriously hurt, if not killed.
And soon afterwards finding out why everyone says Joshua is a Jesus analogue.
"Here comes the Beat wagon!"
As far as I'm concerned, the attack Neku uses at the end of the final battle, where he fuses with all three of his partners and activates a giant skull attack, which finishes the final boss in one blow (and looks extremely cool while doing it) was probably the most awesome moment of the entire game.
In Solo Remix you instead do a Fusion with all three characters, each using the strongest Fusion you have unlocked. Depending on how you spent your Scarletite, this could mean you shoot up Draco Cantus with God Zilla Mr. Mew Eye Beams, crash a tidal wave on him, dropping the freaking moon on him, and then finally finishing the boss off with the skull attack.
Joshua yelling "That's it, you are DONE!" and impaling a giant shadow rhinoceros with a beam of sacred light fueled by the souls of the dead.
Week 1 Day 7, Shiki fearlessly talking back to Higashizawa and stating that there's nothing he can do, she's getting back. Also a heartwarming moment.
Every player gets a personal one upon defeating Bonus Boss Panthera Cantus on Ultimate Difficulty. Don't pretend you don't feel all-powerful once you've finally managed to kick those kitten's asses.
The fact that Progfox does a Fusion by itself is awesome. There's no other instance of this anywhere else in the game.
All of the Level 3 Fusions are pretty awesome. Neku and Shiki ride a giant Mr. Mew that shoots two giant Eye Beams, Neku and Beat ride a tidal wave that crashes down onto the bad guys, and Neku and Joshua drop the freakin' moon onto the enemy.
The soundtrack. Tracks like "Twister" and "Three Minutes Clapping" do an amazing job to back up the style of this game.
Just before the fight with Anguis Cantus, all looks lost, but then... "Here comes the Beat Wagon!" Cue "Twister" playing in the background as Beat and Shiki pull their Big Damn Heroes moment!
A meta one for Square-Enix in the Solo-remix of the game. They managed to make the partner system much, much more useful and allowing the player to control it much more easily. Espically J's.
Konishi keeps on saying that everything goes according to her predictions. And then, Beat, of all people calls her out on this with the fact that there have been so many hiccups in her so-called "master plan" already.
Beat: Then what's wid all these "unforeseen circumstances"? Sounds to me like you can't predict jack, yo.
How about the part where you use Beat on the top screen and the Rhyme pin on the bottom to finish off Konishi for some sweet revenge. These are your only sources of damage at this point in the fight, ensuring that the enemy receives a well-deserved Karmic Death.
Joshua gets a cross series one. The Gang shows up in Kingdom Hearts 3D: Dream Drop Distance and eventually Joshua reveals that the Heartless attacked Shibuya. Unlike other SE characters in KH, Joshua heavily implies that he IS the real Joshua. And he managed to save his friends by flinging them all into another world, another universe. Something he couldn't really do in TWEWY, and that no other character has done in KH. (at least not in the same way)