She saved the drowning child at the risk of her own life.
Literal
She [topic-は] life [possessive-の] danger [object-を] risking drowning child [object-を] saved.
命の危険を冒して (いのちのきけんをおかして, 'risking the danger to her life') is a dramatic expression. 溺れている子供 ('drowning child') is a relative clause. 冒す (おかす, 'to risk, brave') is a literary verb.