The student might be getting a response out of you. Change the way you respond to her. Your questions about what to do in order to "Get" her such as punishment make me think you want to sort of punish her through pain.

When kids complain about you, their audience can either say "Yes I agree this teacher DOES do those things" or "You're stupid. I disagree.".... if you're worried the student is convincing others that you're doing bad things or something... this is an opportunity for you to look in the mirror, check to see what you might be doing, and adjust if there is any ammunition in which the complaining student is correct.

I am NOT saying you're in the wrong. But I've found that bad kids tend to be quiet when they don't get the response or reaction they want. Try not giving them the attention they are seeking if you've been doing that.