I ran in to do this quest and stated randomly killing priests. Then they disappeared and the boss was active.
OK, I think, lets get down to this and I am getting him down to half health, but then he heals up. This goes on for a long time, then I run away!!
I checked up on wowhead and it turns out the best way to solo this, especially if you don't have a dispel, is to make sure the Hydra priest is killed.
I killed the Hydra and then the Hawk and then I easily killed the boss.