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She's making an effort to save up as much money as she can.
Literal
She [topic-は] [as much as possible-できるだけ] money [object-を] [trying to save-貯めようと] [is-making-effort-努力している].
The frame [volitional]＋と＋努力する is a stronger version of [volitional]＋とする: instead of just 'try to,' it makes the trying explicit by naming the effort verb 努力する ('make effort, strive'). Common register for goal-oriented framing — résumés, motivational speech, news profiles. お金を貯める ('save money') uses 貯める, the transitive verb specifically for stockpiling currency or value, distinct from その他の 'save' words like 残す ('leave behind'). The ている marks the effort as ongoing.