She passed the entrance exam for the all-girls high school.

Literal

She [topic-は] girls'-high-school [of-の] entrance-exam [to-に] passed.

入学試験 (entrance examination) is the formal term for the exam taken to enter a school — the casual abbreviation 入試 is far more common in conversation. 合格する (to pass) takes に to mark the exam or institution passed. Japan's entrance exam system is a defining feature of its education culture, with intense preparation (受験勉強) beginning years in advance.