This appears to be the only missable achievement in the game.
When you reach the second world (island/pirate themed) and unlock the town there (Port O'Potty), you will come across a whale that asks you to find something to help cover its nakedness.
This will open up a level that allows you to retrieve some pink bikini bottoms for the whale. Typically, you would give these to the whale to complete the quest.
DO NOT give these to the whale. Doing so will void the achievement and require you to try again on a different save slot. Instead, travel back to the first world and go to the town (Tree Vale). Talk to the old man at the very beginning of town. He will ask for the bikini bottoms and give you his old, used underwear in return.
Take the old man's underwear to the whale. This will also complete the quest and earn you the achievement.
If you miss out on this achievement on your first playthrough (as I did), it's fairly quick getting back to the whale in the story. Ignoring all cupcakes in each level and running through them as quickly as possible should get you back to that point in under an hour.