。
I'll get severely scolded by my parents.
Literal
Parents [by-に] harshly scolded-regrettably.
こっぴどく is the adverbial form of こっぴどい — an emphatic colloquial form of ひどい (terrible/harsh). しかられてしまいます combines the passive of 叱る (to scold) with ~てしまう (regrettable outcome). The speaker anticipates an unpleasant consequence.