She kept dancing all night at the disco.

Literal

She [topic-は] disco [at-で] all-night, [kept-dancing-踊り続けた].

一晩中 ('all night long') uses 中 ('throughout, the entire span of') as a productive suffix — 一日中 ('all day long'), 一年中 ('all year round'), 世界中 ('throughout the world'). 踊り続ける is a compound verb formed with the productive auxiliary ~続ける ('keep doing X / continue doing X') attached to the masu-stem. ディスコ is a clipped loanword evoking a specific era of nightlife — bouclé, neon, the late 1970s through 1980s. In modern Japanese the venue would more likely be a クラブ or ライブハウス.