Superman first appears as a playable character in story level 5: "Chemical Crisis", about halfway into the level. Once you can play as Superman, press the Y button (or cycle with LB or RB (the shoulder buttons)) to choose him.
As Superman, "double jump" (Press A twice) to become airborne. Then move around with the left stick. Use A to increase elevation, and B to drop. You'll get the achievement in less time than it took to read this.