Hit the flagpole at the end of a level when the last digit of the timer is 1, 3, or 6.
How to save and continue
When you die press L + R then select "Save High Score". After that you may turn it off or whatever. When you come back to it at the title screen press A and then start. You will start on the first level of the last world you were on.
World Select
After beating the game, if you do not turn off the console, you will return to the title screen. There, you can press the B Button to start as desired in World 1, 2, 3, 4, 5, 6, 7, or 8.