She's used to staying up all night.

Literal

She [topic-は] all-night do [to-のに] used-to is.

~のに慣れている ('is used to doing') combines the nominalizer の with the particle に and 慣れる ('to become accustomed'). 徹夜するの nominalizes the act of staying up all night, and 慣れている marks the completed state of adaptation — she's already accustomed, not in the process.