He decided that my doing my job well and doing extra work when I had free time was an attempt to make him look bad.
It started out with him giving me the silent treatment for some imagined slight. The first couple of times he pulled this I genuinely thought I had inadvertently done something to offend and apologized. He would "consider it" and eventually things would go back to normal. The third time he pulled this, I wracked my brain and couldn't think of a single thing I had done that could possibly warrant such an overreaction, so I completely ignored his behavior and acted as if nothing was abnormal. I figured if I had done something he could damn well tell me what was upsetting him or just get over it. I told him point blank when he decided to speak to me again that if I did something that upset him, tell me on the spot so we could resolve it instead of him stewing silently and expecting me just *know* what I had done (because clearly I must have done whatever it was on purpose 
).
That, unfortunately, didn't work and I gave up when I confronted him on yet another bout silent treatment and he snapped "Well, I'm mad at you, so you must have done something!" but he couldn't think of anything I'd actually done. There were lots of other things and he was always careful, for the most part, to avoid doing or saying anything in front of witnesses.
The best you can do is avoid being alone with this person. She will likely not attack you in front of other people. Be as nice to her as you can, don't give her anything to twist into a slight or insult. Ignore her snark as much as possible; she sounds like a miserable person who wants to drag you down and make you as miserable as she is. Lastly, be sweet as pie to everyone else you work with so that when she tries to badmouth you to them (and she will) they'll blow off whatever she says.
From my experience, her goal is to provoke you. She wants a negative response (preferably in front of others) to make herself a victim and you the bad guy. Avoid giving her the kind of attention she wants and it will backfire on her. She will appear to be petty, snarky, and unreasonable and everyone will be on your side.
I stuck it out because I was determined to stay at a job I really liked and not be driven away by this guy. He eventually quit and left for another job; he was fired from that job for sexual harassment. (I know it's wrong of me to gloat about that, but *tee hee*).
Good Luck to you!
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