。
She was carefully styling her hair.
Literal
She [topic-は] earnestly hair [object-を] was-setting.
懸命に — 'with all one's effort, earnestly, intently' — is the freestanding adverbial cousin of the famous four-character compound 一生懸命 (the same 懸命 'risk-life' core). It paints the styling as a focused, dedicated task rather than casual primping. セットする is loan-verbing in action: the English noun 'set' gets attached to する to mean 'to style (hair),' a piece of beauty-salon vocabulary now fully naturalized in Japanese. The auxiliary ~ていた frames the whole scene as ongoing in the past — the camera catches her mid-task.