In all cases, the above criteria should be combined with a TEFL (Teaching English as a Foreign Language), TESOL (Teaching English to Speakers of Other Languages), or similar qualification that covers the theory, methodology, principles and practice of the English language training. If you do not meet either of these educational criteria, you may still be able to teach English in Japan if you have several years of experience as a language instructor. Some schools may consider teaching experience as an equivalent to a formal education in the above areas.
So although it is theoretically possible to work in Japan as an English teacher with a TEFL or TESOL certificate but no undergraduate degree, meeting at least one of the outlined education criteria will improve your chances of finding employment.