On the password screen, enter the first three letters of any of the planets (Except Earth and Planet X) to start at that level, with Godzilla and Mothra at Lvl 1. See how far you can get on the harder planets!
When battling Mecha-Godzilla with Mothra, make sure you are lined with his neck and have the tip of your upper wings just to the right of the "A" in "Godzilla", now keep firing your eye beam and Mecha-Godzilla's lasers will always miss and go right through your wings.