、。
She worked hard to make up for the time she'd lost.
Literal
She [topic-は] with-all-one's-might [adverbial-に] worked [and-て], lost time [of-の] make-up-for [object-を] did.
失った時間 is a noun-modifying clause: past-form 失った ('lost') directly modifies 時間 ('time') with no relative pronoun. English needs 'the time that she lost' — Japanese just stacks the past-form verb onto the noun. 埋め合わせ is the noun form of the compound verb 埋め合わせる ('fill in and match up,' i.e. compensate); ~をする turns the noun into a discrete act. The connecting て-form 働いて reads as 'and (thereby)' — sequence and means rolled together.