。
She succeeded because she worked hard.
Literal
She [topic-は] with-all-one's-might worked [because-ので] succeeded.
~ので is the softer cause-marker — it presents the reason as objective fact ('she succeeded because effort caused it') rather than as a personal claim, which suits matter-of-fact narration. ~から would feel a touch more assertive. 一生懸命 paired with 働く is a near-default collocation in Japanese: you almost never just '働く' for a praising context, you '一生懸命働く.' The two past tenses 働いた・成功した establish a clear chain of cause and effect, both completed.