Recommend that your attendings fail her and make sure the PD knows that you did.
Put it in terms of the ACGME core competencies.
Finally someone admits to using the core competencies to address personal grievances.
First off, since she got a "competitive sub-specialty," this intern is probably better than her peers or even her resident, who has just one more year's experience.
But it does look like she has some maturity issues that can be addressed informally by more aggressive means. Sit her down and tell her your concerns. She is being a diva and it is not appreciated.
Failing her by using the core competencies abuses the integrity of those evaluations. It also calls into question your own integrity when you use grades to settle scores.
Medicine is filled with egos, as we all know. It is pervasive because the system selects for high-achieving individuals. When I was in college, the pre-med advisor looked into a full auditorium and said only 1 in 8 of you present will make it to medical school. The undergraduate institution was highly ranked. So this girl made it to medical school and beat most of her peers to get the "competitive specialty". There is no doubt, she is special.
So let us assume that you take a mob mentality approach. You fail her with the worse possible evaluation. You turn her attendings against her and they fail her too. You even get the PD involved. Then the PD calls her residency and they rescind her contract. She's now untrainable and has difficulty getting any other position.
You might feel good that she got what she was due. The profession loses another talented individual who more than likely would have matured as she progressed through the training years.
Rightfully, she's angry but intelligent. She becomes a lawyer and, naturally, is recruited by plaintiff's medical malpractice firms. Given her medical training, she has an easier time picking apart physician expert defense witnesses. During her career, she succeeds in many cases. Physicians call her a traitor. But who betrayed who? Who made who?
So you feel good with yourself that you "taught her a lesson." She may have the opportunity to "teach you a lesson" a few years down the road.
The point here is that the ideals of the profession get abused by its practitioners through their personal interactions. It then becomes important to take a step back. Physicians should be on the same side. They need to resolve these differences without involving formal measures that could end careers. There will always be someone smarter who has a more prestigious job. There will always be a part of you that demands greater respect. But is it absolutely essential to the primary mission?
I would concentrate on making sure she is taking care of her patients well. If you are a man, I would tell her that she is being a diva and it is not appreciated. If you are a woman, then you may have more leeway in the terms that you use to make the message clear.