。
She couldn't overcome her fear of the dark.
Literal
She [topic-は] darkness [of-の] fear [over-に] hit-and-prevailed [thing-こと] [subject-が] couldn't-do.
打ち勝つ ('overcome, conquer') is a compound verb stacking 打つ ('strike') + 勝つ ('win') — literally 'strike-and-prevail.' Used for overcoming obstacles, illness, fear, opponents. The に before 打ち勝つ marks the thing one overcomes (parallel to ~に勝つ 'beat X'). The pattern ~ことができなかった is the standard 'was not able to' construction — combining nominalizer こと + できる ('be possible') in the negative past.