I'll usually damage boost him until he goes up and shoot from below him. Usually I don't have that many left before he's dead. Sometimes I'll get lucky too, and he'll shoot fireballs before he dies giving me a really healthy amount of missiles.
I'm assuming then that you get the third energy tank right before him, because otherwise it seems like you'd die before he goes up. I usually damage boost from him until I've shot ~20 missiles into him and then go over to the right wall. When he goes up he almost always shoots fireballs, so I shoot my four supers quickly before he gets them out, then missile spam until he dies. usually this leaves me with 49 health and 15 missiles as long as I don't do anything stupid.