1) MAKE SURE THAT YOUR TATTOO ARTIST HAS CONSIDERABLE EXPERIENCE TATTOOING. The more tattoos your artist has done in the past, the better he/she will be at tattooing.
2) ASK TO SEE HIS/HER PORTFOLIO. If an artist comes up with an excuse as to why he/she doesn't have a portfolio, it's probably because the artist hasn't done enough tattoos to have any good pictures. Or, the artist may not be very good at tattooing and doesn't want to show you (a potential paying customer) the sub-standard tattoo artwork he/she has done in the past.
3) ASK THE ARTIST IF HE/SHE HAS EXPERIENCE TATTOOING LETTERING. Tattooing Ambigrams (and pretty much all other lettering) requires a very steady hand and someone who is extremely good at straight lines. Be sure that his/her portfolio work shows good, straight lines as opposed to shaky, wavy lines.
4) MAKE SURE THAT THE ARTIST USES A THERMAL-FAX MACHINE TO TRANSFER THE STENCIL TO YOUR SKIN BEFORE TATTOOING. Unless your artist is Michaelangelo or Von Dutch, don't let him/her free-hand the stencil. A thermal-fax stencil will ensure a perfect foundation for your tattoo. Don't settle for anything less!
5 ) A CHEAP TATTOO ISN'T GOOD, AND A GOOD TATTOO ISN'T CHEAP! Just because the shop across town will do your tattoo for fifty bucks less DOES NOT mean you will get the same high quality tattoo as you will from a good, experienced artist. In the end, a good tattoo that will hold up over time is worth way more than the fifty bucks you thought you'd save at the time.
6) TATTOO ARTISTS ARE INTELLIGENT, HELPFUL, AND CREATIVE HUMANS. Listen to their suggestions in terms of placement, color, size, etc. They know what they're talking about and will want you to love your tattoo; and they know how to make it the best it could possibly be.