It depends on who you work for and what you do...and if you can cover the tattoos. As far as I have seen, if you have a tattoo and work for a cruise line you have to cover it up. However, if you can cover it with a band-aid or flesh-colored tape it is fine. I know a musician who wears long sleeved shirts to cover his arm tattoos, and he has been on ships for three years now.
If you got the job and really are worried, find some makeup or bandages to cover the tattoos up, and you will be fine.