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.
Finish the whole damn game.
Collect half the hats.
Collect all the hats.
Finish Shotgun universe in under 60 seconds.
Play through Straightjacket Darkness universe without dying, with a horse head.
Eat every fatcake in fatcake universe with a hamburger for a face.
Beat Rejected Green Clone universe in under a minute wearing a monocle and top-hat.
Dance to the first boss and don't stop for nothing.
Beat the scrolling shooter segment without dying, as a dinosaur.