She is becoming a good instrumentalist, but her aural side is letting her down. How can you help someone work towards improving in this area?
By singing. Loads of it. Get her to join a choir. Singing is massively helpful for training an ear to recognise pitch better. I've done things with pupils before where I've almost "tuned" their voice by getting them to adjust by sliding from where they start until they match the intended note. Also, do work where you ditch the piano and just get her to sing to another singer (that equal temperament thing can really upset some people). Finally, check that the issue isn't just about being able to hit higher notes/lower notes. Transposing the pitch of an aural exercise might make it much more achievable.