Wow, that's a lot of interest around berghia and aiptasia. Here is a method that worked perfect for me and can be started with only two berghia. This is the resulting method from my trial and errors. I had a few thousands aiptasias at the time of the start (200 gal aquarium overfedd with copepod and other stuff). I ordered six berghias in october and in february I couldn't spot any. At the end, I could spot at night a hundred berghias wandering on on every corner of the tank trying to find a last aiptasia. I trade a part of them and the rest disappeard quite quickly (a few week after the last aiptasia).
You only need time. First effect 2-3 month after start. The worst the infestation the best it will work.
Step 0: Check that there is no peppermint shrimp in the tank (eat the berghias). In my experience, wrasses are no problem as berghias are nocturnal, they will be hidden under rocks during the day.
Step 1: Take two (or more) 1-2 gal plastic or glass container and put some seawater from your tank. I personnaly used 20L transparent storing boxes from IKEA with the lid almost closed (a pencil in the corner for gas exchange) but smaller container should be just fine. Place it in a dark (so no algae growth) temperate place (20—25°C). Then capture a few aiptasia without damaging them too much (that's the hard part). Easiest way is to scrape the ones that are on the glass or the one that grows on macro algae. Feed them a little and take care of removing every bit of algae or rock in the container (lot of tiny critter eat baby berghia). This is the crucial part that made the difference between successful culture and nothing happend. Change some water once a week to keep the water quality in check (but not too much, aiptasia love dirty water). When you see around 10 aiptasia from different sizes in every container, order a couple of berghia.
Step 2: Change the water before putting the two berghia in the container. Watch them feast on the berghias for a few days and lay eggs everywhere. When they have eaten half of the berghias, moove them to the next container (use a plastic pipette for capture) . When you run out of container, capture the berghias and place them near your worse infestation spot in the main tank (the best is to do it at night) and cross your finger (Hopefully you will soon spot 20 to 40 new berghias in each container).
Step 3: Wait for one month to six weeks. Cover the container so the evaporation is reduced. If necessary, compensate with RODI and agitate with a spoon so the salinity is even. Don't put any airstone, heater, food. Waterchange is not necessary. Egg should hatch around one week after beeing laid. Then nothing is visible for a few weeks. Use this time to capture more aiptasia and put them in a new container. Do not disturb the containers with the invisible baby nudibranch.
Step 5: One day you will see very small berghias. They will grow quite fast but they get more and more hungry as they grow so feeding them can become a problem. You can capture the biggest and feed them in an other container with some aiptasia infested rock until they are big enough to be put in the main tank. Start making a list of people who will be interested by some of the offspring.
Step 6: Put most baby berghias in the main tank and save a couple to try to raise a new generation in more plastic container... The limit will be the supply of aiptasias. Watch the population of aiptasia receed in the main tank and trade as much berghias as you can as they will soon all vanish...
I will soon restart berghia farming as the aiptasia are slowly back (three years later) so if you are near Geneva Switzerland, send me a message. This time I will try to document a little better the attempt so I may start a new thread with all this.
Good luck.
Serge