Berghia nudibranchs will indeed solve the problem. However they ONLY eat Aptasia, so once the problem is solved... you nudibranch will starve to death. Not a good solution.
Peppermint Shrimp are the ideal solution, because once the Aptasia are gone, they become part of your regular clean up crew.
However there apparently are several different shrimp sold as Peppermint shrimp, and not all of them are Aptasia eaters. I got lucky and got the right ones. They had my aptasia infested tank clean in just a couple days.