Answer:
His name is Diablos. Draw/Cast his own Demi spells back at him, and keep summoning your Eidolons. His own gravity-based spells cannot kill you, as they do a percentage of damage to your lifepoints, the only danger is when he reduces you far enough, then uses a melee attack. But since he favours his gravity spells, it's not hard to recover if he starts getting the upperhand.