She works hard to make a living.

Literal

She [topic-は] livelihood [object-を] earn [purpose-ため], with-all-her-might is-working.

生計をたてる (せいけいをたてる) means 'to earn/make a living' — literally 'to stand up a livelihood.' ~ため marks the purpose: 'in order to earn a living.' 一生懸命 (いっしょうけんめい) means 'with all one's might' or 'as hard as possible' — one of the most commonly used intensifiers for effort in Japanese.