If you managed to survive your first encounter with the Parasite Cage, the next fight shouldn't have proven too difficult. It's essentially the same battle save for the monster's increased HP, poison breath attack and the addition of the damaging acid that coats the floor.
- Jump off a platform and attack the monster with aerial combos (attack from the front as the monster cannot be damaged from the rear).
- Once you land, jump off the ground immediately and retreat to a platform. Attack in the same fashion.
- While fire is effective against this monster, I recommend using magic solely for casting Aero and Cure. Use these spells when necessary.
- When the monster sways backwards, it's stomach will open. Attack the inside of its belly, making sure to pick up any HP/MP balls that may be dropped.
That's how I go about the battle.