To stay up all night in Engpsh can be expressed in a few different ways:

"Pull an all-nighter" - this means to stay awake and work or study throughout the entire night.

"Burn the midnight oil" - this means to work or study late into the night, often until the early hours of the morning.

"Stay up late" - this means to remain awake and active past one's usual bedtime.

"Be a night owl" - this means to naturally stay up late and be active during the night.

For example, you could say "I have to pull an all-nighter tonight to finish this project" or "I'm going to burn the midnight oil and study for my exams."