Most of the workers on the cruse that I went on (royal carribean) were from foreign countries, including the doctor. The cruise line does this so that the dont have to pay workers substantialy. You could always join the Navy.....Now thats one big cruise ship!
I saw a report many years ago on Dateline about cruise docs. They said a lot of them never completed their residence and were not certified to practice anywhere else. Of course there are some retired docs that do it a few years just for fun. I have actually considered it for a retirement job.
As far as you you need to do to become one...pretty much just get through med school. Besides that you don't need many other qualifications.
A friend's live-in nanny's son (Ukrainian citizens) works as a bar tender on Royal Caribbean. They work you like crazy and it's not fun or glamorous like you think it is. I read about cruise ship physicians before. While they get paid reasonably well compared to other people on the ship, they still work a ton and it's not like a big vacation for them. It's better to work hard on land, so you can actually take a cruise and enjoy it.