IDW's Rat King is a bit of a mystery, to this day I have no idea what he's trying to accomplish.
We know Kitsune has a clear objective to ressurrect Shredder as her father the Dragon Lord, but Rat King just seems to cause chaos and mayhem without any real motive. Although I guess that's the point of him as that's his role in the Patheon, just like Toad Baron just likes making extravagant parties with food and have a ball.