The rat king can be severely annoying, specifically the flame thrower part.
Keep it on assist mode to make it a touch easier. There are ten items to deliver and each time he changes up his attack (usually phases of two with increasing speed).
Phase 1: Avoid the little flames on what appears to be a mousetrap board (if you're old enough to know what that game is). I stuck near the top section with good success.
Phase 2: This one is terrible. He does difficult to avoid flamethrower attacks. There might be a pattern but you're on a timer and don't have all day to learn them. Just do the best you can.
Phase 3: Tons of stuff fall from the sky (junk). Easy to avoid. On the way back you'll need to watch out for rockets but they give you lots of time before landing. The downside is the item is difficult to fit through the junk on the ground.
Phase 4: You must time the moving wall with the laser. This too can be difficult but there's only two patterns to learn
Phase 5: Finally, a break! Just navigate between the easy lasers. I don't think I've ever died to them.
Final Phase: Nothing! The rat is unable to harm you. Finish the last item with a casual walk.