。
She tried to maintain her composure.
Literal
She [topic-は] composure [object-を] maintain [volitional-と] endeavored.
落ち着きを保とうと努めた — 保とう is the volitional of 保つ ('to maintain'). と努める ('endeavor to') creates a formal 'tried to' pattern. 落ち着き (おちつき, 'composure, calm') is the noun form of 落ち着く.