Luckily, she got into the university she wanted.

Literal

She [topic-は] luckily-also wished-for university [into-に] entered-school.

幸運にも is a fixed sentence-adverb meaning 'luckily, fortunately' — it adds the speaker's evaluative comment on the event. The も here isn't strictly additive; it's part of an idiomatic adverbial frame: 不幸にも ('unfortunately'), 意外にも ('surprisingly') follow the same pattern. 入学する ('enter school') takes に for the school entered — schools and universities are treated as goals one 'enters into.' 希望の大学 ('the university one hoped for') describes Japanese university entrance culture, where students often have a tightly held first-choice school after years of intense entrance-exam preparation.