This game is about a guy named Jason.

Jason had a pet frog named Fred. One day, Fred decided he had enough of being locked up in a fish bowl and made a dash for the door. As fate would have it, Jason was there when all this happened and he gave chase. Once outside, Jason was totally amazed to find Fred running toward a huge radioactive chest. As soon as Fred touched it, he grew to an enormous size, and the radioactive chest fell into the earth along with Fred. Jason tried to reach for Fred but fell into the hole along with him. 

When Jason landed, he found himself alone next to a huge armored vehicle. This was not just any vehicle, but one designed for the ultimate challenge against the radioactive mutants living under the Earth's crust. These mutants, created from escaped radioactive waste, are controlled by the Plutonium Boss.

Your mission is to fight your way and destroy the Plutonium Boss before he destroys you.

 Along the way to your final encounter are many warlords of the underground you must destroy.

 (storyline from Blaster Master game manual)