From a biblically aesthetic perspective, I usually trot out the question, "Ever heard of gilding the lily?" Jesus talks about the lily as being more glorious than Solomon in all his splendor, and yet it comes to us as God gave it. Is it possible for a person getting a tattoo NOT to be saying, "My body is not beautiful enough the way God gave it to me, I have to improve it"? Would this not then fall under Peter's injunction about making our adornment be not so much outward adornment, but the inward adornment? Of course, Peter is talking to women at that point, but I would hardly think he would then say, "Now men, you feel free to go right on and make all your handsomeness consist in outward adornment." What's good for the hen is good for the rooster.
Ultimately, the desire to become more beautiful needs to be channeled into a sanctifying manner that is primarily concerned with the soul, and yet also sees the body as the temple of the Holy Spirit, and therefore in need of care and nourishment (we do NOT want to go down Plato's blind alley of seeing the body as evil). What we will find is something strange: as the soul becomes more beautiful through God's sanctifying grace, the body becomes more beautiful as well. Kudos to Tyler for mentioning God's mark: we already have a mark of belonging, and it is baptism.