Radical Spectrum Volume 2 continues the story of the siege of Nucleus City by Prince FaceBox. After being chased away by Doc DuBrane, the Box minions regroup around the SineWave tower, soon to be the world's tallest building when it's complete. It's up to Doc to climb the active construction project and use the Prisma Cannon to finally chase off FaceBox and his gang.

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While the story continues, the gameplay departs from the first game. Volume 2 borrows ideas from the next generation of video gaming, primarily taking its influence from Donkey Kong. Doc has to climb single-screen levels, randomly generated, trying to make it to the top of the screen to destroy a Minion Monitor, an iteration of one of the Box Minions that deploys weapons to fight off Doc while larger ships above drop radiation. Doc can absorb radiation and, instead of shooting up as in the first game, now the Prisma Cannon fires down, allowing Doc to double jump, and destroy the Monitors. Every so often Doc will also encounter the larger ships responsible for the dumping of Radioactive Waste. Make it to the top, and destroy the reckless Prince FaceBox!