Bananas first appear on the second stage.
They are dropped by monkeys (appearance changes from stage to stage but they float/fly aimlessly in the sky and do not attack.) they are a rather frequent but still random drop.
Additionally they can drop in any direction they want. Including behind you and down pits.
The achievement is cumulative so don't worry about grinding it out on the second stage or worrying about getting 20 in one run.