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