How to handle this difficult Coworker?

So I am having trouble with a female co-worker who seems to have it out for me and I am not sure what her problem is.

She frequently complains about me to management whenever she gets a chance over the silliest shit wherever or not it's worth complaining about. If i have to work nearby her she will sooner or later complain about something I am doing allegedly to try to get me out of there. When she is doing that she is glaring at me. If we have to speak about something work related she is scoffing and snapping at me or just ignores completely. If she knows I am annoyed at her she usually avoids me when possible otherwise she seems to be around watching me from across the room looking for something else to complain about. Sometimes it's rather amusing how much attention she seems to paying to what I am doing and how botherd she seems to be. She will also hang around my area chatting towards the end of shift generally making shit awkward since I really feel like telling to clear off.
Despite all of this she has befriended all of my friends at work and while initially be a bit of loner she started getting along with a lot more people. So thanks to this I usually can't avoid her since she seems to make it a point to be around so much and if she goes to such extent to dislike for no reason why she keeps being nearby. She seemly has a thing for one of my mates who I know fancies her though nothing has happened yet and it's possible she is just using him for the attention.

The only thing I know I have done to her is binning a drink of hers on the first day she started which just left around I thought was trash and apparently she still remembers this and a mutual friend mentioned she brought it up once whe she mentioned me. But it would be ridiculous to hold a grudge over that.

So what to do about her she refuses to speak or ignores me if I do try to get along and if she does it's usually short and too quiet.
How to handle this difficult Coworker?
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