By the way, I was originally gonna make it completely non-Godzilla, but that would've made things even more boring.
* * * * *
1984 - After a 30 year absence, Godzilla attacks Tokyo again, destroying the city and the JSDF's Super-X. Eventually, however, Godzilla is lured to Mt. Mihara, toppling into the crater just as the volcano erupts.
1989 - The events of Godzilla vs. Biollante play out more or less the same, except Biollante is never killed, since Godzilla never rises from Mt. Mihara. The JSDF is of course keeping a close eye on her, but since she never leaves Lake Ashino, they decide not to anger another kaiju unless neccessary. The Super-X II is still built, but survives 1989 with Godzilla trapped.
1991 - The Futurians arrive and pull the "Godzilla-destroys-mankind-so-let's-make-sure-he's-never-born" bit. While they fail in stopping Godzilla's birth (though he still gets stuck in Mt. Mihara), they succeed in creating King Ghidorah. The Futurians send him to destroy the only creature capable of opposing Ghidorah: Biollante. Biollante tries her best, but is decimated by the three-headed monster. After making short work of the Super-X II, Ghidorah continues his path of destruction across Japan until Biollante returns in a second, more reptillian form. Biollante puts up a much better fight and badly wounds Ghidorah this time, but she is still not strong enough and is beaten by Ghidorah once again, ascending into the skies. Weakly, Ghidorah continues his rampage until, once again, Biollante returns, having achieved a new form.
Biollante finally finishes off King Ghidorah and returns to Lake Ashino, and the Futurians are killed/arrested/whatever.
1992 - Mothra and Battra wake up thanks to the approaching meteor. The following events play out more or less the same as Godzilla vs. Mothra, but when Battra attacks Nagoya, he is faced with Biollante, who senses the threat to humanity that Battra possesses. Biollante manages to drive off Battra, who retreats underground. When the two insects transform into their adult stages, Biollante allies with Mothra and helps her subdue Battra, who finally gives up on killing Mothra and leaves Earth to go destroy the meteor. Biollante returns to the lake, and Mothra returns to Infant Island.
1993 - The UNGCC reveals its ultimate weapon: Mechagodzilla. Based on the very first kaiju to attack Japan, Mechagodzilla is armed with an impressive arsenal of weaponry. However, since it is based off modern technology instead of the futuristic Mecha-King Ghidorah's, Mechagodzilla isn't quite as powerful as seen in Godzilla vs. Mechagodzilla. Rodan makes his presence known as the Godzilla egg is carted off to Japan. Rodan smashes a large part of Kyoto looking for his "brother," but ultimately cannot find him and, beaten by Mechagodzilla, returns to Adonoa Island.
1994 - The crystalline SpaceBiollante arrives on Earth, thanks to B-Cells stuck on Battra. SpaceBiollante decimates a large part of Japan, and is ultimately faced with the combined might of Biollante, Mothra, Rodan, and Mechagodzilla. Though Mechagodzilla ends up destroyed, the Earth kaiju triumph, slaying SpaceBiollante and sending its spores back into outer space.
1995 - A multitude of Destroyahs rise and begin attacking Japan. Godzilla Junior, having been raised by Miki and the UNGCC, is sent to battle them, along with the new Super-X III. Though Junior destroys a few of them, they eventually prove to be too strong. Biollante and Mothra get involved and manage to wipe out several Destroyahs. Rodan senses Junior and flies to Japan and helps him fight the precambrian creatures. Before too many more are killed, the remaining Destroyahs combine into a gigantic final form. The Earth kaiju come together once again, though Mothra and Rodan are killed by Destroyah's power. Putting up the fight of their lives, Junior and Biollante manage to weaken Destroyah enough for the Super-X III's Freezing Masers to finish him off. Biollante ascends into the heavens once more, and Junior takes his first steps off Japanese soil and heads out to sea.
* * * * *
Whaddya think?

