。
She did her best to express herself well.
Literal
She [topic-は] self [object-を] well express [volitional-よう] [quotative-と] did-her-best.
頑張った (did her best / worked hard) is one of the most commonly used Japanese words for effort and perseverance — emotionally charged and colloquial, with a 'hang in there!' energy. 自分をうまく表現しよう (trying to express herself well) uses the volitional form of 表現する, and the と marks the content of her aim. 頑張る is far more everyday than its formal counterpart 努める (to endeavor): coaches, parents, and friends shout 頑張って！ as encouragement before exams, sports matches, or any tough situation.