[Nyororin]

I think the best way to think of it is this;

You don`t need a degree to teach. However...

You need to have a visa in order to work in Japan. In order to receive a visa, you need to have a degree or some special talent that is in high demand.

So... Unless you have some other method with which to obtain a visa (married to a Japanese citizen, etc), you`re going to need to have a degree to get a job teaching. Native English Speaker is not a special talent that will get you a visa.