먼젓번 담임 선생님의 말은 죽어라고 안 듣던 말썽꾸러기들이 박 선생님 앞에서는 고개도 제대로 못 들고 수줍어했다. = The troublemakers who never once listened to the previous homeroom teacher have turned bashful even to look teacher Park in the face. What comes before 말썽꾸러기 is a clause functioning like an adjective, similar to a relative pronoun clause. [[{먼젓번 담임 선생님}의 말]은 (죽어라고) 안 듣던] *말썽꾸러기들* = *the troublemakers* [who would not listen to [what {the previous homeroom teacher} said] (even for a second)] 죽어라고 is a common intensifier adverb, like "to death" in the sense of "extremely" or "desperately". It's a short for "죽어라!" 하고, like " as if you wanted to die / as if you wouldn't even stop at death", but it is mainly a loose intensifier. It doesn't mean death literally. 죽을 듯이 is a less common synonym. - 죽어라고 공부만 했다 = I just hit the books like my life depended on it. - 죽어라고 뛰었더니 일등을 했다 = I ran like there's no tomorrow and ended up winning the race. - 죽어라고 일해 봐야 남는 게 없다 = Even if I work my butt off to death, I don't seem to get anything back.

먼젓번 담임 선생님의 말은 죽어라고 안 듣던 말썽꾸러기들 the trouble makers who used to act up excessively on the previous teacher 먼젓번 : previous XX의 말을 안 듣다 : to act up on XXX 죽어라고 : excessively, by all means

my previous tutor (or class teacher) always said but it is incorrect. I need more information. you should inform me full sentence. It can be changed what word comes next. 전체 문장을 알아야지 해석 가능합니다.