。
She overcame the difficulty.
Literal
She [topic-は] that difficulty [target-に] beat-by-striking.
打ち勝つ is a compound verb fusing 打つ ('strike, hit') + 勝つ ('win'), meaning 'to overcome, triumph over, defeat' — typically obstacles, hardships, or rivals. The に marks the target of overcoming. The 打ち~ prefix often functions as a strengthener rather than literal striking — also seen in 打ち消す ('cancel out, deny'), 打ち合わせる ('coordinate, agree on'). The verb has a slightly literary or formal feel — fitting biographical or narrative descriptions of triumph.