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She drove off the man who came at her by yelling at the top of her lungs.
Literal
She [topic-は] loud-voice [with-で] yelled-and attacked-came guy [object-を] made-flee.
Several layers of compound action here. 襲ってきた is the past of 襲ってくる, where ~てくる ('come doing X') marks motion toward the speaker — the attacker is approaching. 奴 ('guy, fellow') is rough/colloquial and slightly contemptuous, fitting the dismissive tone toward an attacker. 退散させた is the causative of 退散する ('flee, disperse'), so 'made (the attacker) flee.' Causative + violence-related verb is common in dramatic writing.