。
She bravely endured adversity.
Literal
She [topic-は] resolutely adversity [to-に] endured.
逞しく (たくましく) is the adverbial form of 逞しい ('strong, resilient, indomitable'), describing the manner of enduring. 逆境 (ぎゃっきょう, 'adversity') is a somewhat literary Sino-Japanese compound. 耐える (たえる, 'to endure') takes に for the thing endured.