Press Left, 2, Right, Up, Down, Left, Right, 2 at the title screen. The text "World 1" will replace the "Press Start Button" message to confirm correct code entry. Press 2 to cycle through the world numbers then press 1 to begin at the displayed level.
Get all seven Small Diamonds in order from left to right in every level. After defeating the Boss, a secret door will appear. Go inside to get a new permanent ability and a Big Diamond.