This one is glitchy. After playing through the game twice and even seeing the badge on my badge screen, the achievement hadn't popped.
What I found was that I had skipped the cut scene where the parrots transport me to the parrot realm. Therefore, in order to not miss out on this, DO NOT SKIP CUT SCENES.
Just keep hitting Next until the scene is done. There a couple of cut scenes at the end of the game. Just click next through them, but do NOT skip them.