完膚無きまでに is an emphatic set phrase meaning 'completely / utterly / to the point of leaving no skin intact' — originally about battle, here repurposed for a devastating romantic rejection. 振っちゃおう is the volitional of 振る 'to dump/reject' + ちゃう (casual completion) — 'tried to go ahead and dump him.' でしょ seeks confirmation accusingly.