In general female behavior is not explicable in terms of rational pursuit of goals, but as innate reactions to stimuli, at least in anything pertaining to sex and reproduction.
And most things do pertain to sex and reproduction, at least until they hit menopause.
Thus, to explain a female’s behavior, one does not ask “what do woman want” but rather “how would this reaction to stimuli have affected reproductive success in the ancestral environment?”
It is obvious and well known that tattoos uglify women, which has a direct and substantial harmful effect on their lives and reproductive success. So, why?
Well, I can report the reason in one case. The one women where I was around when she made the decision to get tattoos initially wanted to get tattooed as a shit test. Her motivation was to test if I was strong enough to stop her from doing stupid self destructive things. Which I was. And then eventually I dumped her. After I dumped her she proceeded to do a pile of stupid self destructive things while somehow going to considerable lengths to involve me in them. The message being “see, without you to care for me and protect me from myself, I will do stupid self destructive things.”
Well, that is one case, and maybe it does not generalize, but this is the case where I know the reason why a woman got tattooed.