Q: I did better than one of my friends at something she cares about, and now she is saying bad things about me behind my back. How should I respond?
A: When others want to hurt us, that is always because they are sad and scared. If you do not accept this simple fact, you have no way forward, so accept it.
Once you have accepted it, ask yourself in all honesty if the problem you hope to solve is that this person is sad, or if the problem you hope to solve is that this person is able to make you sad. Answer honestly. Either is fine.
If you hope to solve the problem of her sadness, then try to make her happy. This happiness must be real happiness, so pretending that you aren't really good at your skill, or pretending to be closer friends than you really are, won't work. If you want her to be happy, then ask around to find out what makes her happy, and try to give her that or make it easier for her to get it. Be aware that if you are pretending that you want her to be happy, when you just want to get her to leave you alone, then she will smell that from a mile away.
If you hope to solve the problem of her ability to make you sad, then know that the solution to this problem is inside of yourself. There are times when we should take action inside of ourselves to make it harder for others to hurt us. This action is simple: fully accept how she is making you feel, then allow that feeling to flow through you so completely that it doesn't hurt. This might sound crazy, but it works. There are basically two ways to do it.
First, let the pain she gives you become a way to connect with all the suffering in the world. Become a sister to everyone who is suffering right now. In that way, this feeling is a gift. If you push it away, then you are pushing away the experience that links us all. Accept it fully and know that at this moment, we are connected to everyone, since everyone has at least a little suffering right now. This is how we build compassion.
Second, if you accept it fully and experience it completely, it will turn into something far bigger than pain: a sense of being alive that is the ground holding both pleasure and pain. You will notice that both pain and pleasure, when experienced fully, lose their footing and fall into the joy of just being alive. If this joy is experienced fully, it loses its footing as well, and that is the final solution. This is how we build wisdom.
With compassion and wisdom, both the problem of her sadness, and the problem of your sadness, will be resolved.