My improved version (994 frames faster) of the original movie. Going below 3 minutes might be possible with improved planning and better understanding of damage boosting.
Game-end glitch description
The glitch is performed in the "Area 1-1" portion of the 1st stage, during the transition off of the first elevator. While on the elevator, Down+A is held as you transition back up again from the bottom screen (RAM address: 0x200 to 0x00EC), causing your character to fall out-of-bounds into a glitched area of the map. Entering and landing in this area causes the game to execute the ending.
: Accepting as an improvement to the published movie