Successfully complete the indicated task in Planet Superstars mode to unlock the corresponding stage:

Alex Kidd: Successfully complete "Get A High Score!" in the "Space Harrier" stage.
Outrun: Successfully complete "Hit Justice Shots" in the "Virtua Squad" stage.
Space Harrier: Successfully complete Tournament Singles in the "Space Channel 5" or
"Virtua Squad" stage.
Virtua Squad: Successfully complete "Hit The Big Zombies!" in the "Curien Mansion"
stage.