Is this any help? Point being is that the work environment often rewards such behavior, even if such rewards are unintentional. In such a circumstance talking to other managers won't get you anywhere.
As a male, I'm not well equipped to make suggestions in this narrow context. I grew up reading books and spending a lot of time riding my bicycle along back country roads - it wasn't exactly Little League or high school football. Therefore I stood out as 'different', and never made any attempt to suggest otherwise.
In the workplace, the people that resent me think I have some sort of 'unfair advantage' - I seem to know things and be able to do things that others can't. This happens when a software developer is working around people in chemical reprocessing plants or food packing operations. I saw the female to female side of this when my (now-ex) wife was telling me that her boss explained to her that she (the boss) hadn't gone to an Ivy League school or had a debut, etc., etc. My wife, of course, had grown up in one of the rougher parts of town, had total recluses for parents, and only got into the school she did by spending months filling out financial aid applications.
Perhaps the behavior of this co-worker is designed to suppress competition. If so, such effort is only worthwhile when invested at competitive threats. This suggests she thinks you could eventually crowd her out. An appropriate approach then is to differentiate - you don't do what she does (professionally) and vice versa. Carve out a niche where you aren't a threat, but could become 'equal' to her as your skills evolve. This would mean looking carefully at what she does, so you can structure your role to complement it.
Eventually this creates a situation where she can't prosper unless you do, and this would attenuate a lot of the harassment.