To get to the secret island you need one of the following three items: Icarus Wings, Rocket Boots or Innertube.
Once you have one of these items, go back to the first world. To do this just fall of the side of what ever world you are on, keep doing this until you're back at the start.
From here, use the item you have and go towards the bottom left side of the world map, over the water.
After a few seconds you will find another islands with a hole in the middle. Simply fall down this hole and you'll be taken to World 0 and get the achievement.