Here is the full list of all 20 Dr. Oil achievements worth 1,000 gamerscore. It takes around 0-0.5 hours to unlock all of the achievements on Xbox One.
Complete level 1
Complete the first world
Complete level 16
Complete the second world
Complete level 31
Complete the third world
Complete level 46
Complete the fourth world
Complete level 61
Finish the game
Die once
Die 10 times
Die 72 times
Die 150 times
Jump 10 times
Jump 100 times
Jump 234 times
Use the dash 10 times
Use the dash 50 times
Use the dash 123 times