To unlock the following tournaments, you have to win the indicated ones:
Escalation Story Tournament: World Open Tournament
HAR Master (Mantis) Tournament: Ultimate Warrior Tournament
HAR Master (Warlord) Tournament: World Open Tournament
HAR Master(Gargoyle) Tournament: IFL Cup Tournament
HAR Master(Jaguar) Tournament: North America Open Tournament
IFL Cup Tournament: North America Open Tournament
Multiplicity Story Tournament: Ultimate Warrior Tournament
Redemption Story Tournament: North America Open Tournament
Transition Story Tournament: IFL Cup Tournament
Ultimate Warrior Tournament: IFL Cup Tournament
World Open Tournament: Ultimate Warrior Tournament