Berghia Nudibranchs - know up front that if they survive predation (wrasse, peppermint shrimp, other) they will die off once they clear out all of the aiptasia. Also they are a bit expensive in my opinion.
Matted filefish (Acreichthys tomentosus) - may nip at soft corals like Xenia and random zoa's. They may be mistaken for eating other corals like a corky sea finger gorgonian as they clamp their mouth or bit it to stay steady while sleeping. Mine does this and also uses my green star polyps - without damage. I have one from Biota and it does wonders.
Peppermint shrimp - opportunistic eater in my opinion. Work better with numbers but may bother some other fleshy corals that eat like an Elegance. I've had two shrimp try and peel back the polyp when it was eating to steel the food.
My personal preference is the Matted filefish as I've used them a few times with consistent results. They will also eat prepared foods be it frozen or pellet so no worry about starvation when pest is controlled. More so with captive bred as they are already eating both. However my recommendation is to buy the fish because you want it and utility being a plus/bonus.
Note - with all above and mentioned in the thread they will take time. You won't notice it over night but you will over the course of week 1, week 2, etc. Also if you have Aiptasia now you more than likely will always have it as it will be in your sump, plumbing, overflow, etc. Another reason why I like using fish.
Note 2: my opinion, works for me, my experience, your mileage may vary - have a great day.