If you go through stage 1-3 normally there will be coins and pipes on the top of the stage that you can't access. To access them you need to activate two secret elevators.

The first one is right at the start of the stage. Position Mario exactly three blocks away from the left side of the screen. Jump and lean against the wall and there's your first elevator. Stand ontop of the block and don't move. You will go straight through the top blocks and Mario will be on the top of the screen where your stats are.

The second elevator is at the second lion. Kill the lion and dodge the two falling stones. There will be a row of five blocks that go in a pattern of coins and bricks. Break the second brick with Super or Superball Mario. Jump through the hole you just made and the second elevator will appear. There will be no coins this time, but it will lead you to a secret pipe. In expert mode a plant enemy will be there so watch out.