She despaired and gave up.

Literal

She [topic-は] despaired [and-て] gave-up-ended-up.

絶望する (ぜつぼうする) means 'to fall into despair' and あきらめる means 'to give up' or 'to resign oneself.' The ~てしまった ending adds a sense of finality and regret — she didn't just give up; she 'ended up giving up,' implying the outcome was lamentable or irreversible. The て-form of 絶望して connects the two events as a natural sequence: despair led to surrender.