The other endings are meant to be hidden fairly well.
MINOR SPOILERS:
The more overt choices to where the storyline branches are in the Sportsdome - responding to Lanks or Cyclops in a certain fashion will change the course of the story.
Another choice can be made at the very first of the game. Play in Pain Mode again and speak with Rodriguez multiple times. This one is hard to find.
MAJOR SPOILERS (In case you want direct instructions):
To unlock one ending, respond to Lanks by picking all of the TOP (first) options in dialogue for EACH match. (Four times)
To unlock a different ending than that, respond to Cyclops by picking all of the BOTTOM (second) options in dialogue for EACH match. (Four times)
For the last and secret ending, play in Pain Mode. Run from the very first Yogurt Masters fight, collect the item he drops and then go find Artie Choke. Do not kill him - just give him the mags and then speak with him. Trade the item he asks for for a Toolbox. Then return to Rodriguez and you're set.