Pike Balls can be dropped from the Skeleton enemies and can also be bought at the store.
Redjarman confirms that you can use Super Pike Balls.
They have long durability and you should only need about 2 or 3 depending on speed.
You can whip the gel enemies and the eyes on the wall but the Pike Ball must be the only thing that touches the Boss.
Just equip a ball and jump into the eye over and over until he goes into phase 2 and starts flying around. You can't control the ball but if you can get lucky enough to have him strike you while the ball is above he'll stop midattack and back off. Once he lands for the laser you can either duck under it or if he's too low jump behind him. While ducking or behind the ball should just take care of the damage until death.