You need to watch the Chimera's sp bar. If you're not poisoned, use earth armor+shield, as it will attempt to poison you on sp attack. If you're poisoned, it will use the fire breath. If you avoid ever being poisoned (Lucretia's Poison Neutralizer potion can help, and Protocea or Healing Branch can outright cure Poison), the Chimera will never actually use the fire attack.
There are also two strats that can outright cheese the fight:
- Pre-stack Kindred charges and use celerity to crush the monster with 6x damage attacks.
- Haunted Dragonlord's Will shield can give you qc Chi Shield. Cast Purple Rain, spend all your sp and hp on stacking the shield, re-cast Purple Rain. You end up being basically invulnerable.
A slightly less cheesy strat, similar to the one above, is to use Gandolphin. It gives you a qc mp shield, which basically turns your mp bar into a second hp bar. For better synergy, cast Gangolphin in Generalist Robe (with Imbue toggled on) to max out the shield's efficiency, and use Rejuvenating Necklace to avoid running out of mp.