What do you do when a bully tries to get you fired?

I started a new, remote job and very quickly it became clear that my coworker was a bully. She was rude and condescending towards others and she spoke to people in a degrading way. She liked to put people on the spot and make them feel stupid and powerless. Nobody stood up to her because she was intimidating and good at getting you to blame yourself for her treatment of you.

When she tried this with me, I immediately stood up to her and called her out. She apologized, but then started going behind my back, trying to destroy my reputation.

My boss asked me in a one-on-one meeting how things were going with her, and I told him that I had confronted her because I had been seeing a pattern of severe disrespect in her behavior. He didn't believe me because he said he had "never seen" that kind of behavior from her before. He works remotely, so he only gets so much exposure to her and she's very good at putting on her best face for management.

Now I get the sense that my boss no longer trusts me and thinks I'm the bully instead of her. I think that she has worked very hard to slander my name and to get people to turn against me. I don't know what to do, and I'm afraid I'm going to get fired, all because I dared stand up to her.
What do you do when a bully tries to get you fired?
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