Are you in a union? If so, I would ask them for advice.
Keep a log of all incidents. If anything is in email or other written form, even better.
Speak to your manager. I know this won't be easy, but it's what HR have asked you to do, and it's not unreasonable - if you were to raise a grievance (which is an option, and part of why you should keep a log), one of the first things people will ask is, "what has been done to resolve this so far?"
Try to be specific, and ask for that back. "If a piece of work isn't up to standard, I need specific examples to know where to improve." Otherwise, you might be left thinking you need to spellcheck it better, when she's referring to formatting the report structure - and that goes both ways. If you are finding behaviour X is the problem, you need to state that, so she can't assume you're talking about behaviour Y. If she's already giving specific examples, but isn't doing so for your peers, you need to ask to be treated the same as them. There can be valid reasons for doing this - I would expect something like spellchecking work to be a basic from everyone, but other things I would pick up with some people more than others, because people don't all perform the same, and some people need to improve on different areas than others - but if someone is getting pushed to improve different things that others aren't, it needs to be clear why.
This won't be an easy thing for you to talk about with her, so have you got anyome you can practise with, to role play how it could go?
If you have tried raising it with her, you could raise a grievance.
Ultimately, you can search for a new job. If things aren't likely to change and it's affecting you that much that it's affecting your home life, you need to think about how much more you are prepared to put up with.