。
She tried hard to live up to their expectations.
Literal
She [topic-は] their [genitive-の] expectation [to-に] meet [in-order-to-よう] effort-did.
Two patterns combine here. 期待に沿う ('meet expectations,' literally 'go along with expectations') is a common set phrase. ~ように努力する ('try (so as) to do') frames an effort directed at achieving a state. The bare よう (instead of full ように) is a written/compressed variant — both forms are grammatical but the dropped に sounds slightly more terse. The verb 沿う is written here in kana (そう), which is also common.