Learn Japanese with Anime - On Behalf of the Moon, I Will Punish You

Analysis

月 is “the Moon”.

に代わって means “on behalf of”.

おしおき means “punishment” for the purpose of discipline. By adding する you can make it a verb おしおきする meaning “to punish” but する is omitted here to make the phrase catchy.

よ is a sentence ending particle which is used when the speaker wishes to emphasise new information and make listeners become aware of it. When it follows a noun or な adjective you usually add だ before よ. So in this case, it’s おしおきだよ, but by dropping だ you can make it female speech which is commonly used in anime. In real conversations, Japanese language is becoming less gendered so だよ is usually used by both male and female.