An omniscient being known as the Eternal Champion predicts that mankind will soon fade from existence due to the untimely and unjust deaths of key individuals throughout history who were destined for greatness. Seeking to restore balance to the world, the Eternal Champion gathers these souls from time moments before their deaths. The Eternal Champion only has enough power to restore life to one of these individuals, so he organizes and holds a fighting tournament between them, where the victor will be able to regain their life and change his or her fate while bringing balance to the universe, whilst the losers will be forced to "live out" their deaths just as history intended.
Unlike most fighting games, or video games in general, there are no characters in this game who are "bad" or "evil". Each character has been chosen because he or she is either inherently good or has the potential to do great good and change the course of history for the better. Despite the ability to kill opponents in this game, it is not relevant to the story. Much like games such as Mortal Kombat (which pioneered finishing moves in fighting games), the game's "Overkills" are not canon and are simply a gameplay element for the enjoyment of the player. It is actually revealed in a few character endings that some of the fighters had become allies or friends during the course of the tournament.
I remember this game being hyped by sega when it came out but it's really just a boring fighter. Lame characters and stiff controls. Not very fun.