"Bad ass" means tough, strong, very skilled, fierce, and usually with a bad attitude. It can also be a noun describing a person who has those qualities. Most heroes and heroines of US action movies could be described as "bad ass."
"Marine" is kind of like a soldier*. So a "bad ass marine" is a person in the armed services who is "bad ass."
------------------------
* I know a marine isn't actually a soldier, but for the purposes of answering this question for someone who will never actually meet a marine** and just needs the general idea of the phrase, it works.
** If you do ever actually meet a marine, do not call them a "soldier." They hate that.