Considering that Ahzidal is undead, you're right when you think fire would be the best course of action. I know you probably know this by now, so this'll just be for those who are about to face him.
You can use fire against him, but it wouldn't make a difference. Ahzidal's mask grants him a resistance against flame-based spells and/or enchantments. Now, since that's the case, you would immediately assume that frost spells would work. No, they don't. The mask gives him fire resistance, but being undead gives him frost resistance as well. (This to new people playing the game.)
I was a vampire then and still am. So, you can imagine a vampire facing a flame-based undead priest would be a bit of a problem. Here's something (I think) I've noticed. I decided to turn into a Vampire Lord to at least parallel the gap between our advantages. I started blasting the Drain Life spell repeatedly and I've noticed two things: 1: He sometimes staggers when hit directly, therefore cancelling his charging of his overkill fire blast. 2: When he doesn't stagger and manages to hit you, you can gain some of your lost health back. All you gotta do, simply blast Drain Life until he goes down whilst moving around.
It's not a one-hundred percent guaranteed success should you try this, but if not doing this, then I guess you can always get up close and personal with him and just keep the pressure on with continuous power attacks. I it worked for me when I did it a few more times.