First, you need to get Grannie by collecting all 2000 Golden Diamonds and 40 Water Sprites from the Real World.
Then, go to each stage and find its CGA-Land door and enter it. At its end, you will find a Grannie Medal. Collect all 20 present on the Real World Stages and the achievement should unlock.
Here's a tip: The stage door on the selection screen will be orange instead of blue where you have the medal.