It may be hard, but try and get to know the person you dislike. You both could just have differing opinions or views on things. Getting to know them allows you to understand what motivates them to act a certain way or do certain things.
Always understand that the way people behave is not a personal attack on you, it is usually caused by some deep rooted emotional turmoil that they are dealing with, you might have been the person they take it out on. While this isn't acceptable behaviour, understanding that it is not personal allows you to put aside your dislike and get the job done.
Communication can help ease the situation. Usually with people who dislike you and when the feeling is mutual, and both parties are aware of this, setting boundaries can help. If you don't like the way they say certain things about you or a situation, voice it out. This goes both ways. Setting boundaries will ensure you both aren't stepping on each other's toes and are making sure that you can make the best of the situation.
Humans are generally control freaks, they want to control everything. In situations like this focus on what you can control. You can control how you react to a situation, what you say and do, your mannerisms. Focus on controlling those things instead of the situation itself. This allows you to react with utmost professionalism.
There will always be some form of conflict in the workplace. Not necessarily with you, but when there is know what you can do to make a bad situation work is the best way.
Get to know the person you dislike
Understand it is not a personal attack on you
Communicate and set boundaries
Focus on what you can control