Here is the full list of all 9 No Time to Explain achievements.
Finish the whole damn game.
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.
Collect all the hats.
Finish first Shotgun universe in under 60 seconds
Play through straightjacket darkness universe without dying, with a horse head.
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.