Oh boy, we're going into some uncharted territory here... if you thought the LAST one sounded stupid, you ain't seen nothin' yet.
To start off, some shitheads go to an island, where they develop a weather-controlling machine (ya, a weather-controlling machine), however their progress is tampered with, given the sudden appearance of human-sized praying mantises. However, when they eventually do get the machine to where it can function, a radioactive balloon ends up detonating (I don't exactly remember what the balloon had to do with anything, I might edit this later when I get around to watching it again). This causes a radioactive storm, which ends up mutating the already large praying mantises into gigantic proportions; a "Gimantis", if you will... or a Kamacuras, I guess (whatever that is). The Kamacuras end up digging out a giant egg and smash it to bits. Instead of releasing yolk, however, a giant baby reptile thing ends up plopping out, falling on its head. Oh gawd...
The Kamacuras then mistake the baby for a nutritious snack, so Godzilla arrives in order to kick some ass. After killing most of the Kamacuras, Godzilla ends up adopting the baby, which the humans dub "Minilla" (Mini Godzilla). After various hi-jinks and lessons on the life-skills of giant radioactive reptiles, Godzilla and Minilla end up encountering a giant spider, Kumongoa. After blasting the hell out him with their radioactive breaths, the weather machine fills the island with snow and ice. Rather then just go back into the ocean and swim to somewhere that's warmer, they decide to huddle together and wait until the next movie comes out.