There is no problem with tattoos per se according to the rulings of Syed Sistani. Please see this link for further details (English): https://www.sistani.org/english/qa/01336/
In terms of a tattoo with an image of body - In itself it is permissible.
In terms of a tattoo with an image of animals - In itself it is permissible.
In terms of a tattoo on women - again in itself permissible, but if considered a form of beautification must be covered in front of na-mahram (whom a woman must cover and wear the hijab from).
However, tattoos are not something this is appropriate and narrations tell us that they are not approved of.
More here (Arabic): https://www.sistani.org/arabic/qa/0760/