In the books, Hermione’s boggart is failing her classes. Her greatest fear is failing her classes.
However, it goes a lot deeper than that. Subconsciously, I think she believes that if she does not do well and if she fails, they’ll kick her out of Hogwarts and the Wizarding World. So her real fear isn’t failing.
At Hogwarts, she has two wonderful friends who love her, and she is getting to live in an incredible world. She doesn’t want to lose that, and she thinks that if she does bad in her classes, they won’t let her come back.