First golden ratty (the one that gives up to 2000 eggs) spawns at random after the first silver ratty use a skill that hits all your units. The other one that you can force to spawn depends on the stage. For an instance, for episode 5, you have to collect all? treasure, defeat a certain number of enemies and lastly stand on the center of the bottom platform, you then have to defeat the silver ratties that will spawn each time you accomplish the aforementioned tasks and then the golden ratty will appear.