。
She speaks English very fluently.
Literal
She [topic-は] very fluently English [object-を] speaks.
たいへん ('very, greatly') is the formal-leaning intensifier — slightly stiffer than the everyday とても, more written than すごく, and a touch milder than 非常に. Often turns up in expository prose, news, and polite spoken contexts. 流暢 (りゅうちょう) is a な-adjective meaning 'fluent, smooth-flowing,' and its adverbial form 流暢に modifies the verb: 'speaks fluently.' Note that 流暢 and 上手 take different stances: 上手 frames language ability as a skill (good at), while 流暢 frames it as a quality of the speech itself (smooth-flowing). Common collocation is 流暢に話す for 'speak fluently.'