1) The fact that you even want to give feedback on her behavior is probably due to the fact that she's a woman. If this were a man, you'd think he's a jerk but do what he asks. Here, you want to give her guidance on how to be more cooperative - that's not your job, nor is it her job to demonstrate a cooperative demeanor. Her job is to get things done for her boss, which takes me to -

2) She sounds like she's good at her job and cares more about her boss's satisfaction with her than with what you think. So if you are the "no man," she will stop calling you when she needs something. She'll start calling some one else who's willing to give her what she needs for the big boss. That may mean you get fewer assignments. That may mean that even if you're the one most technically qualified to do something, some one else who has a better attitude will get asked instead of you.

3) You gain nothing, and potentially loose a great deal, but trying to act as a bottleneck to what your leadership needs.

I have a peer who I find so obnoxious to work with - she talks at me, repeats herself all the time, is bossy to almost everyone, etc. She rubs a lot of people the wrong way but is unfortunately one of the higher ups right-hand woman so there's no not putting up with her.

My annoyance has gotten to the level that its unproductive, I've realized my reaction to her is NO instead of trying to approach each convo in a cooperative mindset. I don't have to like her but I want to make sure I'm not matching her obnoxiousness with my own.

Any tips for moving past the annoyance and dislike of her? This isn't something I can talk through with her - its her entire personality, not just one general behavior I can give feedback on.