It is the year 30 AX (Anno eXtraterrestrial). Earth has become almost entirely irradiated. Nucleus City is one of the last bastions of mankind. It is a city built using technology the Moon Giants left behind 30 years ago when humanity learned it was not alone. The tech casts a shell around the city that protects it from radiation.
Meanwhile, in space, other beings are watching. The reckless Prince FaceBox has noticed Earth, and, mistaking it for a galactic radiation dumping ground, has gathered his posse to dump his own planet's waste on ours. Along with AutoBox, GlamBox, and ScreamBox, he manages to get his ships passed the shield and starts dumping waste, not caring at all that he's clearly wrong about Earth and there's a bustling city directly below him.
Meanwhile again, local Super-scientist Doc DuBrane has nearly completed work replicating the Moon Giant technology in the form of a body pack and gun that can absorb radiation and release it as a high energy discharge with no radioactive component called the Prisma Cannon. Strapping on this pack, Doc confronts FaceBox and his cronies to save what remains of Earth.
In RSV1, the player takes on the role of Doc in an old-school Arcade game scenario. FaceBox and the other Box Minions descend on the city in their UFOs, dropping orbs of radioactive material of different colors. The material passes through the grid, randomly winding its way down until it drops out the bottom, where Doc can absorb it. Absorbing 3 orbs of the same color in a row fills up the Prisma Cannon's tank and Doc can fire a beam of energy directly up, destroying a column of the grid and creating a space through which Doc can then destroy the ship and move to the next level. Every cycle of all 4 minions causes the game to move faster and faster.