We know this much. The Leviathan being leaves footprints. It can open doors. It leaves a slimy residue. I think the thing has humanoid aspects combined with the multi-headed serpent- aspect, and also some deeply horrific and disturbing overall Lovecraftian aspect to pull it all together - something so horribly demonic and grotesque that the human mind cannot imagine or even fully perceive it without becoming unhinged. The only way for the Leviathan cultists were able to represent it physically, was to focus on sepentine aspect of the creature.
More horrifying than anything imagined thus far in this thread...
Yeah, that would be Lovecraft's...If you want a clear picture, I might advise visiting Wikipedia and typing in "Cthulhu." It will take you to a picture that shows what we're describing.