Actually your complaint is now against the principal for not maintaining an appropriate learning environment. You can very easily go to his/her supervisor with the evidence of the teacher's behavior and a lack of response by the principal.

Check the district's website.

Is there a way to file a complaint against a teacher at the central level? Many parents have complained about a teacher to the administration for several years. She is rude, demoralizing to the kids, and constantly yells at them. She even did this when an outsider was in the room observing a child. Administration has not done anything. These students are fragile and often have slef esteem issues in addition to learning issues. It is not right.