What is so confusing?
A work visa requires a bachelor's degree. You don't have it, so you can't get such a visa.
A working holiday visa does NOT require a bachelor's degree, so you are limited to this. The disadvantage to a WHV is that you have to fit the age range (18-30), you have to prove that you have a certain amount of funds, and the WHV can be used only once for a limit of about a year. (In contrast, the work visa can be renewed endlessly.)
While a TEFL certificate is not a requirement to get hired or to get a visa, it will certainly benefit someone who wants to stay a while and teach. It will also benefit someone who has no teaching background. So, it's up to you to decide whether it's financially within your means to get it. With your lack of a degree and teaching qualifications, you will only be eligible to teach in eikaiwas anyway, and they are the bottom rung of the teaching ladder, so you don't have to worry about qualifications. A TEFL certificate will not get you more pay. Besides, eikaiwas often have their own teaching system anyway, and many provide training on it.
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