Begin Stage 4-1 and travel until you reach the two long pipes hanging upside down. Kill off the Piranha Plants, then swallow Shy Guys until you have 6 eggs. Grab a Koopa Troopa, stand on the pipe which previously held the lower Pirahna Plant, and then spit out the shell between the two lower pipes. As it bounces back and forth, rid yourself of an egg; Shy Guys will begin pouring out of the other pipe and will be bowled over until they begin yielding extra lives.
On any stage select screen, hold SELECT and press X X Y B A. You will be warped to the bonus game! Afterwards, you will return to the stage select screen.