The Trunchbull is like evil walking around in a "brown cotton smock" and "breeches," who "look[s…] like a rather eccentric and bloodthirsty follower of the stag-hounds" (8.4). She's supposed to be responsible for the moral and scholarly education of an entire school, but all she does is terrorize the students and the teachers.
The Trunchbull is a nightmarish version of your everyday principal. She's got authority and she totally misuses it. It's just an average day when she flings someone out a second-story window, or throws a little girl across the playground by the braids. It's not really surprising to find out that she's also the villain in Miss Honey's backstory. Wherever she goes, she's the most terrifying and awful person in the room.
Mr. and Mrs. Wormwood, Matilda's parents, are the first antagonists we meet. We think they're pretty bad until we meet the Trunchbull, who's even worse. While Mrs. Wormwood is mostly just uncaring and unavailable, Mr. Wormwood actively tries to hurt his own daughter. He thinks of Matilda as the bad seed in the family, doesn't want to admit that she could be smart, and won't take her seriously. He's all too ready to yell at her, accuse her of things she hasn't done, and keep her from the things she enjoys, like reading. He's a big ol' jerk, and we won't waste any more words on the guy (except in our "Character Analysis" of him).