How to deal with passive agressive co worker?

I used to be close with a person that is now my co worker, and I have noticed they seem to be passive aggressive. She’s has been constantly messing up on the job I’ve been training her on, yet she says she is fine when I ask her if she needs any help. It’s gotten to the point where I don’t think she even cares anymore (possibly her ego is hurt). It frustrates me because she talks behind my back saying that I am a back stabber and not telling her when she is making mistakes—- which is the opposite because I constantly correct her, which probably upsets her as well. She also does work “half way” sometimes or “forgets” to do it, yet doesn’t do it right away.

My question is: how do you deal with a passive aggressive person at work?