Pile Up! Box by Box

The parasols can be found in Frogipelago (First main world) as well as one in Boxling square (the over world). I got this achievement after beating the game in which the parasols were all open but no achievement. I had to hold dash/charge to hit the parasols in order for them to close and then reopen. Surprisingly, the achievement unlocked when I closed the overworld's parasol as it was open by default when I was searching.

From memory, all the parasols in Frogipelago can be found after finding the first frog and before finding the second frog.