If you work in a hospital, try to get as much certified training as you can on specialized pieces of equipment. Usually, that will mean you have to go TDY and travel to various parts of the country. It's fun. You get to attend classes out of uniform. It's like a mini-vacation and you get paid for it. Much of it also carries over to the civilian world as well.
As far as boards go, you will have to study on your own time or ask your fellow BMETs to quiz you on random board questions. Unlike some other departments in the hospital, which might be able to give their soldiers time off to study for boards, you have an important job that is essential to keeping the hospital up and running.
Now is the best time to take college classes. Since you are in a hospital, you are less likely to be involved in ridiculous formations at oddball times. You essentially have a steady day job so your nights are free. Perfect time for studying for classes or the board.