I remember I unlocked it while playing the game on 360. I remember it was very early in the game, I think before I had even beaten the Forest light world.
I have a feeling I got it after beating my first warp zone, but don't hold me to that. From what I can find on it though, it seems like you do need to own the game and can't unlock it with the trial version.
You can also get a Brownie gamer picture by beating Brownie in-game, and your own little Meat Boy avatar prop from defeating Dr. Fetus and finishing the Light World.