It depends on the character. Ven has Faith and Salvation which do damage and heal, though against the bosses in this arena, it's better to do them from a distance since you can be knocked out of Salvation and Faith only has a short invincibility period.

For Terra, unlock his final normal deathblow (the one where he summons meteor). When the boss summons the cage, attack him but don't use skills so you don't accidentally activate one of the Styles instead. Once you get his death blow activated, it keeps Terra completely invincible when using it, hits multiple times and does fairly decent damage with the right weapon. Aqua is stuck using the normal strategy but I guess it wouldn't hurt to activate Blademaster to get some extra damage in.

The main thing is just getting his pattern down. You've technically reached the point where levels are not as useful as skill and some of the bosses actually go up in level with you. The biggest thing with the bosses of this stage is just to keep your distance and learn your timing. Terra oddly enough has the hardest time cause his dash move has pathetic invincibility so he needs to rely on its speed to get out of the way. Ven just needs a minor proper timing with Dodge Roll and Aqua is just a matter of spamming Cartwheel cause it's the best in terms of avoiding damage. Also make sure you're not using the offensive versions of these moves cause they sacrifice invincibility time for the ability to cause minor damage.

Really, the best means of taking them down is keeping your distance, using shotlocks when they summon the cage, occasionally attack the cage to build back your shotlock and have all the damage modifiers that raise the shotlock gauge when you take damage.

Another, albeit risky strategy, is to use the Ice cream Donald's nephews sell cause they automatically put you into one of the Styles. Most of the character's ultimate styles will do a fair amount of damage but you may end up trading blows.

Personally, you need to memorize the pattern of the first boss cause you fight a nastier version of him in the final round...

If you need practice with dodging. I recommend beating the game with all three characters and trying your hand at battling Vanitas' Shadow cause that mother smurfer is a cheap bastard and insanely fast but he'll teach you quickly how to dodge and keep distance in a fight...