Castlevania 3 Alucard Doppelganger fight

This is how to beat the doppleganger boss in Castlevania 3 using just Alucard. Most strategies I've seen on this boss involve switching characters or using Trevor, and I've never found one for just Alucard. I made a save state before this battle and wasted a ton of time figuring this out. I almost wrote this off as being impossible. The doppleganger Alucard tends to wander around for a few seconds, then lock into place. Once he locks in, he will just stand there and fire off energy balls as fast as he can. Unfortunately, his energy balls have priority over yours, so the only way to hit him is from above or below in between his shots. Once hit, the doppleganger will move about for a bit, then lock into place again. I try to get him stuck on the top platform, and attack from below. Attacking from above or constantly switching positions usually led to us just trading hits, which is not good enough. The right platform is larger, and easier to get him stuck there. You have to be careful not to go left when he moves, or else he could jump down. Also, time is very close here. If he spends too much time wandering, you may not kill him in time. He occasionally wanders for 5-10 seconds before locking into place, and that can be killer.