Successfully complete Worlds 1 through 10. Go to Hollow Diamond, then turn 180 degrees and go slowly up the ramp. Land on the narrow platform below, then turn around again and hit the red gate (Meteorite Mayhem). Go to Converse, then move towards the right edge. Wait for the red platform to pass its vertical angle. Gain some speed and dash at the red gate (Big Bang Boom) to unlock World 11.