。
She worked her hardest for her family.
Literal
She [topic-は] family [for-のために] with-all-might worked.
一生懸命 is one of Japan's most beloved compound expressions. Originally written 一所懸命 ('staking one's life on a single place'), it dates back to the medieval samurai code where a 一所懸命の地 was the patch of land a warrior would defend with his life. Over centuries it shifted to 一生懸命 ('with one's whole life') and broadened to mean 'with all one's might, putting everything into it.' Today it's used freely for anyone giving their all — students, athletes, parents, employees. The phrase carries genuine cultural weight: 一生懸命 effort is widely admired, regardless of outcome.