[Sumippi]

大学に入る為に一生懸命勉強します sounds fine to me but I wouldn't say 大学に入るように一生懸命勉強します. I'd say 大学に入れるように一生懸命勉強します.

But...what's the difference? Hmmm...

I think （〇〇する＋）ために is rather polite and preferred in a written style, while （〇〇できる＋）ように sounds a bit colloquial. (Wait, you can also say 大学に入れるよう、一生懸命勉強します, which would sound more formal and bookish.)

I think it's something similar to the difference between 'I'll study hard (in order) to pass the entrance exam' and 'I'll study hard so that I can pass the entrance exam.'