Complete 22 levels without dying. If you go to Chapter Select, the game will show if you completed a level without dying. If you do not have this by the end of the game, you may replay missions and complete them again without dying to get credit for this.
Note: Some levels in the chapter select will not have a death count in the stats. These will not count towards your 22 levels without dying. There must be 22 different levels with a death count of 0 in the stats. I unlocked this halfway through the Realm of the Flappers.