You don't need a raft of academic degrees to become a computer animator. If you have a knack for design, computers, and art, and can back it up with a portfolio of good stuff, you'll have a shot at finding a job.
That said, if you want the all-important patina of professionalism, you might want to spend the time and money on a bachelor's or even graduate degree in graphic design. A concentration in some kind of computer skill wouldn't hurt, either. Credentials like these, plus a killer portfolio, will help you get your foot in the professional door.
The upside about a profession that doesn't formally require any education is you can start right away. With animation, that means just practicing—draw and design in your spare time. If you can, get ahold of an animation program to learn the basics. Passion is the key in an industry like computer animation; if you practice and work hard to learn how it's done, you should be able to find yourself a job.