。
She made up her mind to try again.
Literal
She [topic-は] again to-attempt thing [object-を] heart-decided.
心決める ('to make up one's mind, resolve') is a compact, slightly literary form of the more common 心に決める. 試みる ('to attempt, try') is heavier than ~てみる ('try doing,' a common verb auxiliary) — 試みる is a deliberate effort, often paired with weighty endeavors. The nominalizer 事 (こと) wraps the whole phrase 再び試みる into a single 'thing' that can be the object of 決める. 再び ('again') is a slightly elevated alternative to もう一度 ('once more') — the kind of word that fits resolutions and second chances rather than casual repetition.