Sodium hydroxide
Sodium hydroxide (lye) can be dissolved into RO-DI water and used to kill Aiptasia, either by injection or by coating the anemone. The Red Devil brand, if available, seems to work well. It is sold as a drain cleaner.
When mixed with water, this chemical will release a lot of heat. For safety, mix small quantities, perhaps a few milliliters of water, in a heat-resistant container, and always add the sodium hydroxide to the water. Adding water to sodium hydroxide can cause the water to boil and spray a caustic solution onto you. If mixed in large quantities, the fumes can be dangerous!
Sodium hydroxide will damage or kill any organism it contacts, so be careful. Like calcium hydroxide, it can form blobs that circulate around the tank and cause destruction if they land on a coral or other organism. This chemical will raise the pH and add alkalinity to the tank, so start out with small amounts, perhaps a 1ml syringe, and watch your water parameters carefully and frequently.
Most importantly, this solution can be very dangerous to people! Avoid any contact with skin or any other part of you. The warnings on the Red Devil container are quite serious.
Kalk and pickling lime
Kalk and pickling lime are calcium hydroxide, which is used by some reef-keepers to supplement alkalinity and calcium. It can also be used as a caustic agent to destroy Aiptasia.
Either a paste or a strong solution can be made using RO-DI water. When the calcium hydroxide is mixed into the water, some heat will be released, so be warned! Either preparation then can be injected into or sprayed onto Aiptasia using a syringe.
Note that this solution will destroy any living organism it encounters, and blobs of the solution, if they form and circulate in the tank, can land on your prized coral, anemone, etc. Also, this approach will increase the pH of the tank and add calcium and alkalinity. All of these secondary effects can be dangerous. Start with a small amount of solution, perhaps 1ml syringe, inject only small portions, and watch your tank's water parameters carefully and frequently.
The kalk preparation is also dangerous to you. Be careful with it. Eye contact is the main danger here, but skin contact should be avoided as much as possible.
Quicklime (calcium oxide) can be used in the same manner, but it is much more dangerous. The combination of quicklime and water produces a lot of heat, so be sure to add the quicklime to the water, not the other way around, and be careful about skin and eye contact. Calcium hydroxide is likely the better choice. The tests for this article did not include quicklime.
Vinegar
Vinegar is acidic, and can be used to kill Aiptasia by injection. It seems to kill very small (1/4") Aiptasia by spraying, as well.
This chemical can lower the pH of your tank. Use small quantities, perhaps a 1ml syringe, inject small amounts, and monitor pH carefully.
Hot water
Hot water is reported to kill Aiptasia when injected. Some testing will be done in the future, but time limitations prevented any research for this report.
Hydrogen peroxide
Hydrogen peroxide is an oxidizing agent, and might be effective against Aiptasia. It will burn any organism that it contacts, and will flow rapidly in the water column. The safest approach is likely injection, but caution is advised. Compared to the alternatives available, this chemical seems less useful, and thus hasn't been tested yet, so more guidance is not available.