Personally I'm not a huge fan of Berghia any more ... they're tiny, easy fish food (lost $275 worth of Berghia in 1 night to ..... SEA HORSES! sheesh!) -- wrasses will go after them non stop -- and, they're pretty darn expensive!
I love the filefish but in my experience, they always go after zoas, so tough call ...
So! what's the final verdict?
Peppermint Shrimp! yes, some people haven't had success with them but as zenfish said, there are a couple different types and only certain ones go after aiptasia. So what I do, is ask the store owner to put in some aiptasia with their peppermints (I have yet to see a store that does not have any aiptasia in their tanks so this is usually not all that hard of a problem); peppermints, if going to eat it, will usually go to it within a minute or two max, and start devouring it.
If they eat the aiptasia, great! home they come! If not, on to the next store!
Downside of peppermints is they are voracious scavengers -- they will literally pull food out of lps corals as if they've been starving for years! But the positive side of this is, they're super easy to catch!
Leave a trap with some food in it at the bottom of the tank at night, and I pretty much guarantee they'll get in there
Hope that helps!
- Archit