After completing the first class quest on your world a new NPC called Garrick will appear in the tavern in Ravencrest.
Talking to Garrick will task you with a quest to collect 5 Iron/Lead, 5 Gold/Platinum, and 1 Ruby to help build a map device. Bringing these materials back to Garrick will give you this device, as well as a map to enter with it.
You can use this map with the Map Device to open a portal to the King's Domain.
Garrick's page will explain the quest, Kill the King.
Once you defeat the King Slime you can now receive the King Slime Domain Map as a global drop.
This will allow you to fight through the King Slime Domain once again.