I just eradicated a tank covered in them with peppermints. The secret to guaranteed success with peppermints is to not feed anything, though. Tough on a system with fish (this one is just for this purpose, so no fishes). They wont leave any anemone (including nice rock anemones you really liked, etc.) in the search of food. I tend to overload the tank with them when I go into eradication mode.
Berghia verruciccornis nudis only target Aips, and they work great, too. They won't do it fast, but you'll eventually notice that you have fewer and fewer Aips until they all appear to disappear. THen the nudis die and a straggle Aip reseeds the tank. That'd be the case with anything short of drying the rock out, though, I think.
I believe that a Scat is Scatophargus argus. It's brackish water fish but you can acclimate it to salt water in a relatively short time. It eats aiptasia and some algae as well.
I have a baby Raccoon Butterfly (barely over 1-1/2 inch in length) in a small tank to take care of rocks with aip's. I got him to take care of a recent aiptasia outbreak in my 15 gallon tank that started from rocks that I got from a friend. He is a cute little guy with a boratious appetite for aiptasia and majano/tulip anemones. He may nibbles on other soft corals if he runs out of aiptasia and tulip anemones. That's why he is in a separate tank for this specific service. I can frag off any corals from a aiptasia infested rock and put the rock in his tank. When he is done with my aiptasia, I will have to find him a new home.
Pickling lime (kalkwasser) paste works well, but it's not perfect. It usually takes a few tries, but with patience you can eliminate aiptasia.
I tried peppermint shrimp a number of times, but they have been kinda hit-or-miss for me. Some people have had great successes with them, though.
I have tried Peppermints as well with mixed results. Unfortunatley, I have something in my tank that loves Peppermints. I have found all 6 dead in the bottom of the tank over about a 1 month period.
Thanks to Jack and Kathy for the Kalk powder, I got home from the swap and started on getting rid of the Aptasia. I havve so many that it still looks like I haven't made a dent in them yet. Hopefully this will work over a period of time.