Having a degree is really the way to go. The Japanese government (and society in general, for the most part) are not keen on having people in country that aren't here for specific purposes. That said, there's great support for undertaking studies in Japan as well. I don't think you'd want to live in Japan without a degree anyway. . .what kind of job would you do?
Check out my
blog about life in rural Japan, another good alternative--they need English teachers too and the rent is MUCH cheaper.