I get that you're fresh out of school but your grades don't matter in the real world. I've always felt that 90% of what you learn as a nurse you learn on the job, so you and she are really on equal footing right now.
When I graduated from nursing school
I used to joke that I knew less about being a nurse as a graduate than I did when I first started school.
It is a truly humbling experience to be out there on your own as a new grad.
You may be feeling a little of that and your co-worker may as well. I hope you can try not to make this about school, because if I were her, knowing that you are thinking about her failures, I'd be feeling a little condescended to also on that end.
But I do agree with the others that no matter what the dynamic, it is important to establish boundaries, and it sounds like she is trying to get the upper hand with some of her questions.
Hopefully, you can find a way to look at her as just any other nurse who is being disrespectful, rather than a former classmate, and not get sucked into any games.
You can take control of report by sticking solidly to the subject matter and not allowing yourself to be dragged off on a tangent.
So if she asks you a question, answer it and then keep in your head the strategy that the question was asked, the question was answered, and let's move along now because we're wasting valuable time here with this silliness.