When the game shows Little Mac's knockout scene, press the 1 and 2 buttons together as soon as it starts (regardless of whether or not Mac is about to be TKO'd) or press the minus button at the right time (only works when Mac is about to be TKO'd). This will cause Mac to stomp his foot on the ground and gain one final burst of energy, letting him continue the fight and deny the KO.
The trick can be used multiple times a fight. This can not be used on normal knockdowns; it can only be used during Mac's KO animation.
It should be noted however, that whether or not it will work is completely random, even when executed properly by the player.
This trick will work when the crowd is cheering right after Little Mac starts his knockout animation.