Is it permissible for me to pray for someone to die because I don't like her? Or is it haram? There's this person I hate and want to die, but when I pray will they get accepted?
You should try to befriend that individual and do good. Maybe help them out and if it is because of a serious problem then just try to avoid that individual. Just remember that Allah is watching you and knows what you are doing all the time. If you hate someone turn to Allah and ask Allah for help. Instead of asking to kill the person why not ask to resolve the problems between each other. There has been a question somewhat similar to yours that has been previously asked. If my answer wasn't enough check this out. Am I allowed to make Duaa against someone ?
There is a tradition that when the Prophet was asked about evil that he replied, why do you want me to think about evil, one should think about the good.
Likewise I don't think that it is appropriate to pray for 'someone to die.' If they are a cause, of some injustice to you, then I'd advise praying for that injustice to be recognised and removed.
It maybe that you are a cause of injustice to them. It's only Allah that knows all the secrets of the hearts of men and women. This is why in Islam, He is the final arbiter. In a sense, all judgement is deferred until Judgement Day; though of course, men and women must try for justice in this world too.