When I was doing the English teaching thing, I didn’t have to have it authenticated, I just submitted a photocopy of my degree, and on the back had to write “same as original” and then sign my name. If you need it for applying to university or graduate school here, your guess is as good as mine. I’ve been told that I need to do it, but not really sure when it has to be done since the person I spoke with at NTU said it can wait until after the entrance exams and doesn’t have to be done at the time of applying, while a classmate of mine who applied to the university program at NTU didn’t have to have his high school diploma authenticated at all. I think the important thing here to remember is that this is Taiwan, and “rules & regulations” don’t have the same meaning here as they do in many western countries, and can often be avoided or circumvented if you talk to the right people, have good excuses/explanations, or whatever. I wouldn’t worry about it.
As to where you have to do it, though, you need to take or send it to your regional Taipei Economic & Cultural Representative Office (Taiwan’s pseudo-embassy) in your country of origin. It’s not done directly by the Ministry of Foreign Affairs here.