Others have suggested ways of preparing a unified confrontation with this person. That may, or may not, improve your workplace.
I suggest doing something on a more personal level. Keep in mind that this is business. I would say it's "just business," but it's also your working life so it isn't "just" anything. But dealing with difficult clients is a highly valuable soft skill for contractors.
(I don't know why people call it a soft skill. It's hard! :-)
When you receive anger or anxiety from her, reflect it back, but mildly. Don't be defensive.
For example, suppose she says "What's the matter with you? Why didn't you finish that TPS report by noon? Are you stupid or something?"
You can reply, "Thanks for the feedback. I'd like to do my best to make your job easier. I was working on the ABC account earlier today, and I will do the TPS report now. Is there anything special I should know about it?"
The point is to always make a reference to helping this manager succeed. Don't say "you know I want to make your job easier," because she will hear that as "you are supposed to know I want to make your job easier, but you don't."
You can even say "It seems like you're concerned that the department's work is not going well. What can I do to help improve it?"
Doing this is hard. But the mindset you need is to remember that none of this angry / anxious behavior is about you personally. This particular manager doesn't have the soft skill to take her personal anxiety about her job and her team and use it constructively. You, as a consultant / contractor, can help her learn to do that. The first step for you is to teach her you're working to make her successful.
Now, this may not work with this person. Or it only may work very slowly indeed. People don't change in the blink of an eye. In the meantime, do your best. When you can't stand it any more, complete your contracting engagement and move to the next one.