My grandmother hated tattoos. I got one on my leg when I was in my early 20s. She saw it while it was healing and we got into a fight over it, but it was there and it wasn't like it was going anywhere, so she got over it eventually. At first she wanted it covered whenever we went out together, but eventually she stopped asking me to do that.
If you're close to your parents, I don't think a tattoo will ruin your relationship. If they get upset too about a more visible tattoo, you can always off to cover it if you go out with them once it's healed. There's makeup out there specifically made to cover tattoos that works great, and the compromise might help them be more accepting of highly visible tattoos until they get used to the idea of them.