I'd like to share a method I stumbled onto that kills aiptasias too.
First let me say I had some success with peppermint shrimp and filefish. The problem for me was that they both go after other stuff that I didn't want them eating. So after removing them, the aiptasias came back. I then invested in Berghia nudibranchs, which also are effective, but awfully expensive. They are, in my opinion the best aiptasia controller, and an elegant, natural solution.
Then my tank got ICH. I decided to treat it with hypo salinity, in my display rather than QT, as I was unable to catch the fish.
Long story short, two weeks into treatment, and my aiptasias are gone. So I will toss this method into the ring! Hypo kills aiptasias.
Obviously, this method will not be practical for many, but it is another way to do it. If you are in a situation where you don't mind treating your whole display, this could be an effective (and cheap!) alternative.