Here is the full list of all 9 No Time To Explain Remastered achievements. It takes around 5-6 hours to unlock all of the achievements on Windows.
Collect all the hats.
Dance to the first boss and don't stop for nothing.
Finish Shotgun universe in under 60 seconds.
Beat Rejected Green Clone universe in under a minute wearing a monocle and top-hat.
Eat every fatcake in fatcake universe with a hamburger for a face.
Beat the scrolling shooter segment without dying, as a dinosaur.
Play through Straightjacket Darkness universe without dying, with a horse head.
Finish the whole damn game.
Collect half the hats.