New can be difficult
A new idea can be difficult with a concept like this, especially since Godzilla has been around and smashing for over fifty years. Maybe you can try a different source though. Like the Rampage games, especially total destruction with the bonus characters. How often do you see giant wolves, or bulls?
You can try thinking in view of your game world. Are you going to be using a world from scratch, or your own take of the champions universe? If it's the second, then think about your own villains. Any villain who work with genetics, cybernetics, or machines? The first and third could actually attempt to create a monster of their own, quite possibly by accident, or could lose control of it. In the case of the second, they could create one from the remains of an existing one, or from parts of some other large creatures.
Maybe you could try other source material. Watch some good old episodes of Power Rangers. Have something of interest to one of your players some how get turned into a monster.