Have you ever dealt with someone who actively disliked you?

Avoid, but do not cower.

I had coworkers like this, and I would have to just straight up tell them I'm doing my job fine and that snickering at me for doing a job I know how to do shows that they don't know the best way to do things.

People like this creep me out.

If you can avoid her, do that. However, the main piece of advice I can give you is to not be too passive when you feel you are being disrespected. Keep your behavior professional — don’t do or say anything that can get you in trouble, but you have to sort of assert your dominance in cases like these. People like that back off instantly.

I had a boss once who seemed to hate me (he hated everyone). Once he asked me to do something that was against company policy and right in front of the customer I firmly said “No, I’m not doing that.” After the customer left he called me back into his office. I thought he was going to berate me for insubordination (in front of a customer, no less), but he practically got down on his knees and begged for my forgiveness. After that he treated me a lot better.

I see a few good answers so far, and they are all sensible and well-considered.

Here's another take: don't play fair in an unfair situation.

Your coworker is hellbent on creating a situation that puts you at a disadvantage. She is watching you closely. Do you think she wants to play fair? Fuck no.

So don't play fair with her. You could watch her and report any unprofessional behavior on her part to your manager (assuming you have the same manager). She is bound to do something at some point that's unprofessional. And when she does, you let the manager know. If you can get away with it (and ONLY if you can get away with it), exaggerate or straight-up lie to make her sound worse than she is. Leave a paper trail of her professional failings/violations. (Remember, creating a hostile work environment, in the U.S., is technically considered a professional violation.)

In my experience, people like your coworker are hiding a lot of wrongdoing. Maybe all it takes is a "well-meaning" complaint (on your part to the manager) to expose her and get her fired.

Better yet, if you can, make an anonymous complaint about her.

When I come across someone who dislikes me, I just try to avoid them without being obvious. It might also be good to avoid being alone with them as people tend to behave better when there are witnesses. When I have to interact with these people e.g. if we're both at the same social gathering, I just make polite small talk. I don't tell them anything very personal about myself because I don't want to give them any ammunition against me. To answer your question about whether you should be nice, I would be nice but superficially nice, if you know what I mean. Be respectful and polite but don't kill yourself doing favours for them because trust me, it won't be appreciated.

Grey rock. Be boring to them.

Please document everything. Adult bullying especially at work is real and it can cause PTSD if it gets worse. Obviously don’t go to your super if you can avoid it, but if you start to lose sleep, etc it’s time to shut it down. I’ve been bullied at work. Ignoring them makes it worse. Standing up for yourself makes it worse. They want to hurt you, and they’re going to until it gets boring for them or they get fired. Bullies are scum. I’m

Sorry :(

Yes, my former boss. I tried every tactic imaginable, grey rocking, mirroring her, working hard, working less, etc. etc. - nothing really worked long term. I had to leave eventually.