。
She was fired for neglecting her duties.
Literal
She [topic-は] duties [object-を] neglected [because of-ため] was-fired.
Two notable patterns here. 職務を怠る (しょくむをおこたる, 'to neglect one's duties') uses the literary verb 怠る. The ~ため connects cause and effect: 'because she neglected, she was fired.' 解雇された (かいこされた) is the passive of 解雇する ('to dismiss, to fire'), treating the firing as something done to her.