。
Don't tattle on me.
Literal
I [of-の] tattling [object-を] don't-do.
告げ口 ('tattling, telling on someone') is a compound noun — 告げる ('to tell, announce') + 口 ('mouth') = 'telling mouth' = 'tattling.' 告げ口をする is the light-verb form 'to tattle.' The 僕の here is 'about me' — 'tattling of me' = 'tattling about me.' な is the plain-form negative imperative particle — strong and masculine.