Tattoos are placed fairly deep in the dermis. A TCA peel is intended to remove the epidermis and the stronger ones the superficial dermis. If a TCA peel went to the depth of the tattoo you would get a nasty scar.
Lasers have pretty much replaced other means of tattoo removal like salabrasion (using salt to r;ub off the tattoo) or surgical excision.
The Candela Corporation seems to have an excellent device to remove tattoos in their Alex TriVantage laser. This works for the wavelengths of all the colors of the tattoo.
If you have this done make sure you consult with someone who has eilther this laser or another laser which matches up with the colors of your tattoo.