Instructions
Enter into the level as caped Mario and play through it until you get to the green Star Block.
Hit the block right after the Star Block; a vine will grow out of it. You won't be climbing the vine, but hit the block anyway to make sure that you are at the correct place.
Hold down the "B" button and run to the right. Press the "A" button to jump and fly.
Press the "Back" button on the SNES control pad and continue pressing it to keep Mario in the air long enough to cross the cavern.
Hit the three blocks after you land to get three 1-up mushrooms. Jump through the white gate to beat the level the secret way.