I’m not a good player, but I’d recommend qualifying the battle by shooting the ramps, but don’t start the battle. Then, continue shooting the ramps (lower-risk shots) to qualify the building lock. Then, shoot two balls into the building, but don’t start the multiball. THEN, start the mode and only THEN start Godzilla multiball.
GZ multiball is relatively low-scoring in my experience, but you can get loads of the shots done, especially for Ebirah, when you’re in multiball.
If you’re on a roll (and are s**t player on a roll, not a good player on a roll), you can qualify the building multiball several times, thereby allowing you to complete lots of things without aiming too hard (if you’re a good player on a roll, you can get to Planet X).
I find MechaGodzilla multi-ball to be higher risk to qualify unless you’re really struggling to hit the scoop - at which point, fill your boots shooting it. But, again, if you look like you’re about to start it by accident, stay away from that area until you’ve got something else (like jet fighters) going on.