There's a mistake. I put "I don't know what to do to become a nurse" and it wasn't accepted, but "I don't know what to do to to become a nurse" (with two "to's") was accepted.
I would say you need it. để means "leave the burden to."
Tôi trở thành một y tá = I become a nurse.
That's what you tell your friends once you have become a nurse. But để trở thành một y tá is a process. It requires your conscious efforts.