I was killing small aiptasia left & right, using concentrated lemon/lime juice. However, tiny new aiptasia kept appearing. That is, however, until I bought a Peppermint Shrimp. I haven't seen a single aiptasia in a month.
One caution on buying a Peppermint Shrimp, I have read that some places sell "Camel Shrimp" as Peppermints because they look similar. Camel Shrimp do not eat aiptasia. Make sure you are getting a real Peppermint Shrimp.
By the way, the Peppermint is eating regular fish food, flakes, pellets, & brine shrimp every day. They don't need aiptasia, they just like them.