The option that has shown the most success over the years is to hire your own monster. If you're city is known for being destroyed by a certain monster find it and wake it up. It's true that you run the risk of increasing the collateral damage to real estate but what do you care? There will be one less monster in the world and if you're extraordinarily lucky they might both die. Realistically though only the invading monster will die, the reason is simple. Home court advantage, works for sports teams, works for professional wrestlers, works for gargantuan, as a general rule gargantuan are extremely territorial and will never allow another be in their territory unchallenged.
People want to call out the military; if there is nothing else that we have shown it's that small arms are useless against these creatures. Generally it takes nothing shy of a missile to even get the creature's attention, which makes senses based on their size. The point that I'm making is that if you are calling military strikes you are wasting time, bullets and lives. The only exception is if you are Japanese. The reason is that I know for a fact that Power Rangers, Gundam Wing and the Big O aren't just entertainment; they are instructional videos on how to properly pilot mecha. If you have a four hundred foot tall robot that might, just might be enough to combat the threat.
Your military is much better used setting traps wherever you can accomplish. Pits lined with explosives have shown some success in battling these creatures as well. If you cannot set a trap, you cannot summon another monster and you do not come from a country that has produced bipedal tanks capable of traveling on any terrain without difficulty your options are severely limited. There are two things left and honestly both of them are long shots. The first what the military minds are going to be suggesting from the get go. Nuclear weapons. Now I want you to remember, the reason why this snapping turtle went from two feet across to two hundred feet across and capable of flying like a rocket by pulling its legs into its shell and firing radiation beams out is because it had a run in with nuclear power. I think you run a significant risk of just making things worse if you nuke the creature. The other is hope that science has a sudden break through. Considering that science is what got us into this problem in the first place it can often help us get out of the same situation. One time there was a pollution monster and we erected fifty foot speakers and played the "Safety Dance" until the creature died of boredom.
There is one last thing that I should tell you before I cut you loose into the world and that the all too common event that the monster you meat is something that is unprecedented. Such as bout two years ago when some monster ravaged New York, it sent out small hunters into the sewers. Basically you had all the problems of a gargantuan and a zombie infestation and since the strategies for surviving them are so different it lead to a great deal of confusion. When you come upon those situations I can only say to you that I hope you survive long enough to write your own addendums to this guide so that if I find myself in your situation that I can survive.
