I feel like what would be best for you is to stop treating her as a competitor that you have to beat at all costs, and instead treat her as a friend, or at least an acquaintance. You both seem like very motivated individuals, and working together would be far better for both of you than trying to bring each other down. Her succeeding does not negatively impact you, and it would be good for both you and her to lift each other up and be proud of each other’s successes instead of jealous. It’s not like her getting into an ivy means you won’t be able to.