The *****! Work Colleague From Hell!!!!?

In the US you might be able to file a workers compensation claim or go out on disability for stress. Not sure what your laws are. Check with your local government authorities.

Hate to say it but you need to find another job. Management might get the message if everyone just quit their jobs. But may be not. You need peace of mind and that might mean looking for another job.

If the Management won't do anything, then that is it. Time you looked for another job.
UK

1. Discreetly ask a manager why she hasn't been fired yet, why she's allowed to behave the way she does. Maybe her knowledge or skills are so good, they can't do without her. In that case, you could work to learn all she knows, so they can replace her with you. Maybe she's related to the owner of the company or someone higher up. Maybe they are taking her through the disciplinary process to fire her but are afraid of a lawsuit.

2. That doesn't mean you have to take her maltreatment. You can just refuse to deal with her when she speaks to you wrong. You can just ignore any email or assignment from her that isn't done civilly. Or you can smile and put a friendly spin on it. "Glad to, Maria" - that may be just what she needs to calm down. It may take days or weeks of using this tactic before she responds. And if she's yelling because you didn't do something exactly the way she expected, just smile and say, "I'll fix that for you right now." If she flat out insults you, you can either use humor, "I love you, too, dear" or "I'll keep your constructive criticism in mind." (said without attitude)

3. Read up on behavioral conditioning and develop a program to change her behavior. Consider it a private project and see how much you can get her to change.

It's unreasonable of you to expect her to be fired - she's clearly mentally ill and deserves an opportunity to become well again and then continue her employment.

"She brings her personal problems into work and makes us suffer for it"
You have the option of ignoring her or walking out the office citing an unhealthy working environment.

"takes time off for stress, causing the rest of us to burn out"
It's mangement's fault that they do not bring in sufficient resources when they're a "man down". If you're given too much work to do for your safety, then obtain some medical evidence. Probably the first port of call for that would be your GP. That you're using expletives here shows that you probably really are quite stressed - can you see your doc this evening or tomorrow?