Here is the full list of all 9 No Time to Explain achievements.
Dance to the first boss don't stop for nothing.
Finish the whole damn game.
Collect half the hats.
Collect all the hats.
Finish first 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.
Beat the scrolling shooter segment without dying, as a dinosaur.