That fish in the basketball hoop was still alive. He must've been out of the ocean for over a day at least. Lazy-Eye Larry was firing the Apache chain guns. Sidewinders blow up on proximity fuses. They wouldn't have kept going.
Sidewinders have almost no explosive force.
They're meant to pop aircraft, not cause major structural damage to the Chrysler Building. The devastation of Chernobyl caused earthworms to increase 17 percent in size. That's a lot of nuclear testing to make Gojira that big. A shaped charge would have blown halfway through Godzilla. They could have shot Godzilla in the left eye with current military accuracy at a range of 10 or 20 miles.