Hi OP, I'm sorry to hear about your situation at work. I've been bullied twice in my working life, and I know exactly how it feels. The nitpicking, the micromanaging, the damned if you do, damned if you don't, not knowing which course of action to take and how to preserve your sanity while all that craziness is going on.
The first time I was bullied I was very young, and was on probation. I stupidly resigned and left without another job to go to. I wouldn't recommend anybody to do that in a million years. I ended up with clinical depression after that experience.
The second time was a couple of years ago by a new line manager. I had been in the job long enough and was a union member so I went to the trade union for advice. They arranged a meeting with the bully and she never attended. She left the organisation after that meeting invitation and never came back. She knew very well what she was doing.
Of course your situation is unique but a good starting point is to understand that you will have to "manage" your manager from now on. Make a note of all the comments, how they made you feel, all email communication with her, all one to one meetings. For every behaviour of hers, you need to have an example. Communication by email is a very important piece of evidence so always write professionally and concentrate on work, and try to demonstrate that you are doing your job properly. So if she complains about your work, you've got the evidence that you are doing it.
As you are an agency worker, your situation is quite vulnerable. If you don't have a HR department, it's going to be very hard to fight through the formal procedure. But you need to make the agency aware, and if they employ her too, it's in their interest to know what she's like.
Bullies know exactly what they are doing, and when you name the game, sort to speak, they are cowards. Cannot you arrange a meeting with the people from the agency and her to discuss the issues? She would be quite concerned for her job too if that happened.
In the meantime, keep applying for other jobs and try to get out of that toxic place. What about a admin support role in the education sector, a college, primary or secondary school? They always need office work in education.
Good luck and I hope you manage to leave that job with dignity.