Name anything that she has done that is illegal, other than "hitting people."? Clue, there's nothing. Talking ugly to your supervisees is not illegal. Yelling at people is not illegal. Being a jerk and arguing, verbally abusive, even, is legal. You have no idea why management is allowing this? Well, it is her management technique, and perhaps it's working. Perhaps her area is known for being productive. Perhaps this is where they put people in the beginning of their employment with the company to test whether or not they'll stick, continue to work hard in trying circumstances, etc.
Remember, this is her management technique. Perhaps it is working. Nothing says she has to be nice or act nice to bully people into being productive. maybe it works. Maybe she weeds out all those who would respond in kind, and that's what they use her for.
Your only alternatives are to be polite, professional, and DON'T respond in kind. If you find it necessary, ask to be moved. Tell management why you're being moved, but do not see it as a bad thing if you are "fired" by this person when you do nothing but work and do the job to the best of your abilities. DO NOT let her goad you into stupid passive aggressive behavior like coming in late or being absent too often, or just up and quitting, which means they got rid of you, without having to pay possible unemployment benefits. Being fired for an unreasonable reason, by a bad supervisor is NOT the bad thing you imagine it to be.
But at the same time, it's not your job to fix the problem. You say she is the lowest paid supervisor. She may be on the last stages of her write ups and may be out of the workplace in a short time. What happens to her is NOT your problem, it's management's problem. If they decide to tolerate it, so be it. If you decide you can't handle her behavior, so be it. Don't take up other people's problems with her and be the one who has the biggest problem with her. You cannot fix a bad work place. You may outwit, outlast, and manage to cope with a bad supervisor, but you can't get rid of them legally for the company. They have to do that.