If anyone badmouths her, I won't let them get away with it.

Literal

Her badly say person [subject-が] existed [if-ら] won't-leave-alone [masculine-ぞ].

悪く言う奴 means 'a person who badmouths.' ただじゃおかないぞ means 'I won't let them off easy' — a threatening promise. ぞ adds masculine force.