She worked at the cost of her health.

Literal

She [topic-は] health [object-を] sacrificing worked.

~を犠牲にする ('to sacrifice X') is the stock idiom for trading something dear in exchange for something else. The te-form 犠牲にして here links to 働いた as 'work while sacrificing — / by sacrificing —,' the same manner-/means-て structure that lets you string actions and conditions together: 雨に濡れて家に帰った ('came home soaked'). The sentence reflects a recurring theme in Japanese commentary about 過労 ('overwork') and the social cost of putting one's job ahead of one's health — a theme tragic enough that the language has the term 過労死 ('death from overwork') as a recognized phenomenon.