I've worked with that and don't have an answer for you. I generally avoid people like that like the plague. I would just say as little as possible to her, not talk about her, and just keep your head down and do your job. I don't think if you engage her that there's any way that you will win - 'The squeaky wheel gets the oil' is often true so if she has reason to belittle you etc, people might listen. Therefore, stymy her. Just stay out of her way. People will eventually see what's what and judge her accordingly; it's just that sometimes it takes a while.
I worked with someone once who was much the same, only she had no reason to be jealous, other than her new boyfriend and I had been good friends for years. We worked together for a while and one night, at a company dinner, she sat there and zinged one-liner putdowns at me all night. I didn't respond once. I just let the silence grow and began eating again, so her comment was the last one in the air. I don't know what anyone really thought about all that, but remember, whatever comes out of her mouth is about HER, not YOU. Take some comfort in that - we are all our own walking advertisements.
Another co-worker did mention to me the next day that she looked really petty and everybody wondered what was up, but since I didn't respond, they just attributed the problem to her.
Funny thing - I'm getting married in 3 weeks and my friend is, of course, bringing her