LogFAQs > #977172294

Here's a list of all the rewards you get for beating each boss rematch

Belome - Mallow Weapon
Punchinello - Bowser Weapon
Booster - Geno Weapon
Cake - Autorevive accessory
Johnny - Extra shiny stone (used to challenge 3D Culex)
Jinx - Accessory that boosts gauge generation
3D Culex - A Key Item called Crystal Shard which does nothing >_> You apparently can rematch him though and he'll rank you based on how many turns it took

I'm guessing the weapons are gonna bring everyone else on par with Mario's Lazy Shell and Peach's Frying Pan