Beating the square-cube law it's easy: just allow the surface to grow at a good ratio of the volume. Go distributed and/or go flat and/or get a fractal 'skin' surface.
Examples:
- supercolonies - ant, bees, coral
- clonal colonies - Pando - the trembling giant, Oregon humongous fungus.
Are they monsters? They are certainly big.
And they are able to do damage? I don't think the trees invaded by the fungus are happy. See (or watch) also The Swarm for a potential example of how fast the damage can be exacted.
Now, how big? How about a coral supraorganism the size of Europa, with the energy obtained from the tidal heating?
Will they develop a nervous system? I suppose that's not impossible, even if there will be no "brain" (as the centralized location of "processing", but a distributed/diffuse one. With nodes resembling an octopus'es brain (scroll to "The ‘Brain’ of Cephalopods – An Outline and a Summary of Novelties"):
In the octopus, as far other cephalopod species, the ‘brain’ is assembled through a series of ganglia of molluscan origin to form lobes that are fused together into masses
interconnected by dense (still distributed) networks like the enteric nervous system (that second brain that gives one "the feeling of guts").
Will they develop intelligence? Very likely, although their intelligence is unlikely to be comprehended by a human intelligence. Because an intelligence is formed by the direct experience in the interaction with the environment and one must admit that the two ways of sensing/interacting with the environment (human/monster) differ too much.
Will it develop technology? Unlikely. Too adapted to its/their environment, there's hardly any evolutionary pressure to drive towards the technology.
But assuming it does, I don't want to think of a conflict between Earth and a planetoid sized organism, able to move the hosting rock through interstellar space to get here.
But maybe you, the hard SciFi author, are tempted to think about it?