Requirements for a foreigner working at H.S

I really searched the forums to see if this was already covered, so if someone can answer me or direct me accordingly, I thank ye.

I was reading the thread about what would be required to secure a job working at a university (I’m not even close to there; 4 year English degree from USA, 2+ yrs teaching at kindy/buxiban in Taiwan), but I was wondering what it takes (legally/realistically) to work at public (or are private the only legal way) high schools in Taiwan?

Thanks, in advance, for anyone who can englighten me.