Easy
Godzilla's weak point is the crummy T-Rex arms. That and his large size can be used against him.
The spinal ridges provide an advantageous approach for climbers using rope hook systems. Crampons can be secured between scales to prevent being completely unseated by unforeseen circumstances. These small climbers would be less noticeable than a mite on the human body, due to the lack of skin sensitivity on the scales. A team would be sent to the spot on the neck between the shoulderblades of the beast. This point would be the most difficult for him to reach. The team would be equipped with mining drills, crowbars, and one bigass needle. The point would be to either pull apart the scales there or drill an opening to place the needle. Then a simple pump could inject the creature with a potent neurotoxin. I'm not up on my lizard physiology, so the specifics of this chemical are up in the air at the moment.
Is this feasible? Let's do a quick calculation with some assumptions. Assume that Godzilla's chemophysiology is similar to that of a very large human. We could inject something to freeze his joints and nerves before killing him. Something like botulinum toxin. This is a good idea, because there is a lot of this chemical available in the world as Botox. How much would it take? The reported mass of Godzilla is 164,000 tons (source Popular Mechanics). This is 148778297 kg. The LD50 of botulinum toxin is 1.3–2.1 ng/kg intravenously or intramuscularly (source wikipedia) in humans. Since we assumed the human equivalent, this would mean we need at most 312g of Botox to have a 50% chance of killing it. That isn't very much. We could increase that significantly to have a higher kill chance.
This is an excellent post.. ^^
Delivery would be easier by missiles because they would act like giant syringes. OR we could pump the stuff up his nostrils via a --Nebulizer-- missile..
The only potential misstep here, is assuming that Godzilla would be weak against botulin toxin..
According to most movies, Godzilla is highly Radio-Active, which means he's a walking germ-killing machine..
It's like the radiation is part of his immune system killing foreign contaminants.
Is botulin toxin going to break down under intense radiation. ?
Overall, I believe nothing is immune to brute force..
So if we consider the "time" it takes to defeat Godzilla a crucial factor, cuz he could destroy MANY cities while we figure out how to come up with a complicated plan..
M0ar missiles seems like a better plan because we already got a ton of that stuff..