This will be a companion question for How plausible is my monster?. My previous question dealt with a story treatment for a hard science and realistic take on Kaiju/ giant monsters. While that story does feature Kaiju genre elements, it's really more of a western take on a monster with heavy implementation of classic horror tropes. On the flip side of this is a story idea I had along side the above mentioned story around the same time- a full fledged traditional Kaiju story.
Unlike western monsters, Japanese Kaiju are often times god-like in nature and behave more like forces of nature rather than animals. Often times possessing some sort of breath weapon or at least some form of natural (or rather unnatural) directed energy weapons. They more often than not possess hide extremely resilient to conventional weaponry and overall are seemingly impossible abominations whose tamest spit in the face of all known laws of science and physics. As such in this universe we'll likely never have to worry about a Godzilla like organism rising out of the sea and ravaging our cities...but what if one did?
What if an impossibly huge beast crawls out of the ocean and doesn't crumble into a pile of organs and broken bones the moment it takes a step on land? Not only is it walking around just fine but it apparently isn't even fazed by bombs or missiles. How are its bones not shattering with every step? How is it able to withstand its own internal pressures? How is it able to properly regulate its body temperature? Any answer to my previous question had to rely on at least speculative science and up to very convincing pseudoscience to work, as giant monsters past a certain size or power level are going to inevitably be implausible. And that's fine, good stories don't need to be realistic as long as they follow their own internal logic.
To make this a little easier I'll give a brief description of the creatures.
The Kaiju range from 100 to 600 feet tall
They have no set morphology and come in varying shapes and sizes, as a group appearing to be comprised of creatures that vaguely resemble monstrous fish, reptiles, and even mammals and birds
The Kaiju's skeletons are light weight but are stronger than any metal known to man
Each Kaiju is powered by an integral organic nuclear engine
Most Kaiju can fire a particle beam from their mouths
The Kaiju hide is super tough and resilient
So my question is this: Without resorting to magic or making them alien constructs, what sort of Applied Phlebotinum can I add to my story to convincingly explain away the above attributes and the common problems a Kaiju would realistically face in real life?