At 614 HP you can survive Flare and Masamune, but you'd need to use Cure every round and if the turn order got screwed up (as in Apollo decides to go last one round, then first the next) you'd eat two attacks in a row and get killed. Presumably it's enough HP to survive the explosion he uses too, but it would have been nice to have some elaboration on this as it's the first I've heard of a monster being able to solo Apollo.
Ha ha ha, sorry, I completely forgot to come back to this. Whoops!
Anyhow: of all the monsters that can cure themselves, the Naga is the only one with a *low* enough AGL to predictably go 2nd every time (almost), and enough HP to survive one round. Other monsters with higher AGL will all vary their turn order.
Naga is short one Cure to outlast Apollo, so you have to use Heart at some point. But you don't need it for the other characters, not even Dad; if he isn't around, Apollo's desperation explosion won't usually kill you if you have full health or close to it.