Well its a question of whether they are visibly tatoo's or not, I know crew members who have tatoo's but they are on their back or shoulders, where they cannot be seen in uniform. I believe this is fine.
As long as they are not seen I "think" you should be ok, but I dont know your specific cruise line policy.
If however you have it on your forearm or shins then this could be a problem, if your uniform is for excursion or sports staff you may wear shorts.
If its something like a tattoo on your neck that I have seen becoming more popular, well....I think you can kiss goodbye to working on cruise ships.