I'm sorry you're so worried and hurt. It's hard for both parents and kids at that age to figure out how to separate and shift to a new kind of adult relationship.
To play the other side, she's 18 now, so it's her decision about what to do with her body, and there are far worse things to do with yourself than get a small tattoo that won't show when you're wearing regular clothes. I'm sure you've raised a bright and thoughtful daughter and she'll make decisions wisely (at least most of the time - all of us made some mistakes when we were 18, it's part of the process of growing up). I don't have any tattoos, but I know for my friends that do, it's not marring their skin; it's making an important statement that they want to carry with them always. Even if it's just something fun that she might wish she hadn't done in a few years, it's not the end of the world. None of our bodies are 'perfect', even when we're young, and it's a lot of pressure to put on a young woman to have an unflawed body, especially in today's climate of unrealistic beauty and body standards.
She's not your baby anymore, and if she's anything like me, trying to control her behavior inappropriately will backfire and push her away from you faster. I remember when I was a teenager fighting mightily with my parents - my mom especially - about getting my ears pierced. For a while they insisted I had to wait until I was 18, and I finally convinced them to let me earlier if I got it done at the doctor's office rather than at a piercing place. Too bad the nurse didn't really know what she was doing, used the same auto-gun they had at the mall store, and had no idea how to advise me how to take care of them, so I spent until my early 20s having periodic infections, until I met friends in college who had 'serious' piercings and taught me all the things I was doing wrong.