I worked as a game critic for a relatively large website (as big as they get if they aren't owned by a larger company), although it was all volunteer work to gain experience. The advantage was I got free video games and movies to review, but the work isn't all fun and games. In fact, it's difficult, and because I didn't see the point of researching and writing about Arctic Thunder for XBox or some other crappy game, especially when there are so many reviews out there that'll probably end up saying the same thing, I was able to find out early that it wasn't the career path for me.
Being a critic involves a lot of writing, and although you may enjoy film and video games, you may find you don't enjoy writing long articles about them.
If you still want to do it, then I'd recommend a bachelor's degree, writing for a decent sized game review site, your school newspaper, a newspaper internship, and you're probably going to need to work at another newspaper before a magazine like GamePro or a website like IGN will hire you.