The rules at tiltforums are pretty helpful.
I’d say a great initial strategy is to qualify and lock 1 or two balls into the building, then Shoot ramps to start the jet fighter hurry ups, and complete 5 jets in order to light “collect ally”. (You can apparently also make (?) repeated loop shots to light ally as well).
Trap the ball on the left flipper. Select the Anguirus ally using the right flipper. Shoot scoop using left flipper, without hitting right flipper again (changing ally by accident).
Collect Anguirus. Start gaiju battle. Lock remaining balls into building ASAP.
Multiball starts while you’re battling gaiju. Hit the lock bar button as soon as you drain to 1 ball, Anguirus ally buff restarts the multiball.
If you complete the gaiju battle, the “Raid” insert (Monster Monitor inserts in the Center of the playfield) will be lit solid.
You can now shoot the scoop to change cities if you wish to progress through four cities to “Planet X” mini-wizard mode, or remain in the same city, aiming for complete destruction (requires bridge completion, tanks, and the Power/Tesla strike modes)
Hope that’s useful?
Edit: Forgot to mention that while in the Godzilla/Building multiball, make sure to hit the Mechagodzilla spinner for add a ball!