Berghia were 100% effective for me, and it's a little amazing to hear folks say they were ineffective. Of all the modes and predators listed in this thread, Berghia are the only obligate predators. Berghia are precision marksmen. Everything else is a shotgun-in-the-dark approach.
I will say this. I purchased 8 Berghia from a well-known, semi-local (to me) source. I put them in a 5-gallon aquarium with a bunch of aiptasia harvested from my display. I started by feeding them 10-12 aiptasia per day. They started laying eggs within a couple of days, and after a month I had so many Berghia I could not count them nor harvest enough aiptasia to keep them fed. There were literally dozens of them of all sizes. I started putting them into the display and the sump, keeping the smallest ones in the 5g aquarium to feed. At one point I seriously considered buying aiptasia cultures to keep them alive, but my LFS helped out by giving me a few pieces of badly-infested live rock. At the end of 2-1/2 months since my purchase of the original 8, I had sold about 100 to my LFS and my entire system was aiptasia free. That was about 12 years ago, and I have never seen another aiptasia since.
Here, in my opinion, are the keys. Berghia are pretty sturdy little guys once they establish themselves in your tank. However, they need time to establish themselves. They are very prone to getting blown around by high flows, and are easily sucked into powerheads and overflows. You must reduce your flow in order to give them a chance. Your corals will not disintegrate from this. I turned off all flow except for the sump return pump, and even that I turned down about 50% for the first 2-3 days after adding them. Some other animals will prey on the Berghia. They are a nice little snack to many fish, shrimp, crabs, and other critters. This includes the peppermint shrimps that somebody convinced you would eat all of your aiptasia but never even gave the stuff a second glance. You should add the Berghia to the tank during dark periods so that they are not immediately seen as food to those other predators. They can be eaten and stung by corals (even by aiptasia), and they have a very methodical approach to dinner time. When you put them into the tank, place them on the barest, safest bit of rock you can find. It matters not at all if there is not an aiptasia in sight of them. They will cruise off into recesses in the rockwork, and will quickly find the aiptasia.
If I was confronted with an aiptasia infestation again, there is no question that I would do exactly the same thing as before. 100% effective, and a completely permanent solution. It was also easy, and fascinating to watch them, as well as to observe their life cycle.
