This one is called "Suffragette", and is awarded for completing chapter 7 light world, "The Cotton Alley". This world opens up after beating the boss of world 6, and has easily the hardest normal stages in the game. You're locked into playing as Bandage Girl here, but she plays almost exactly like Meat Boy only faster, so there shouldn't be much adjustment needed.
Be warned, these stages are on the whole even harder than world 5. There's no boss, but you must complete all 20 light world stages.
EDIT: Thanks Kouerson and Misfit119 for pointing out that she does, in fact, play slightly differently from Meat Boy.