She loudly cursed.

Literal

She [topic-は] loud-voice [with-で] abusive-language [object-を] attached.

悪態をつく ('curse / use abusive language') is the standard collocation, with つく ('attach, put') as the verb that pairs with verbal emissions — paralleling 嘘をつく ('tell a lie'), 溜息をつく ('let out a sigh'), 悪口をつく (variant of 悪口を言う 'speak ill of'). The つく family of verb-noun collocations is worth knowing as a pattern. 悪態 is a relatively bookish word; in casual speech you'd more often hear 悪口 or just 罵る.