Personally, I would be very careful about going over her head. Many (most?) sucky bosses are paranoid about this sort of thing for various reasons. Generally speaking, they are afraid (with good reason) that if there is contact between their subordinates and superiors outside of their control, the superiors will start to realize that Sucky-Boss is indeed a sucky-boss. And don’t forget that your boss can often screw you without you even realizing it.
For what it’s worth, here’s what I suggest:
Assuming that quitting is not an option, I would first try and find a way to make myself indispensible to the company. If you’re the only one who understands some complicated but critical piece of machinery; if you write an annual report on some esoteric subject for a company bigshot; if you organize some critical event (and only you know who the key contacts are); or heck, if you’re the only one with health insurance claim forms (I once knew of someone in this position), you are much less vulnerable to Sucky-Boss.
Next, you need to get yourself transferred away from Sucky-Boss. Don’t tell anyone the real reason why you want to get away from her. That won’t get you anywhere. Instead, manufacture some credible excuse to go to a different area - you want to learn a new skill, or maybe it’s for medical reasons. If you’ve made yourself indispensible, chances are a reasonable-sounding request will be granted.
Last, put together an exit strategy. Because let’s face reality - when you’re working for a company, you are always at the mercy of some sucky-boss. If you develop your skills and resources to the point where you can make it on your own, you will find sucky bosses to be a lot less annoying. You will almost hope to get canned.
Short story: you need to make the company dependant on you, and to make yourself independent of the company. If they need you, but you don’t need them, you are in fat city.