While you'll eventually run into most quests in Rune Slayer, some are hidden away in secret parts of the map and you must dig these places out to initiate the mission. One such challenge is the Lost Party quest and its objective to defeat the Rat King, and here's a detailed post on how to find both.
To find the Rat King boss and the initiator for the Lost Party quest, you must visit The Rat Pit and talk to the stranded NPCs there. The Rat Pit is situated deep inside the Pinewood Thickets and below is a step-by-step guide to reach this cave. Firstly, you'll need a Lantern to explore the dark cave. It can be obtained as a reward by completing the Mandrake Menace quest at Ali's Farm in Wayshire.
Once inside The Rat Pit in Rune Slayer, light up your Lantern by pressing H on the keyboard so you can see clearly. Navigating the cave is quite easy, just beware of the rats who may bite and deal minimal damage to you. Walk down the narrow passage, turn left, and jump over the wall.
Eventually, you'll reach the spot I'm at in the above picture. While the left arrow indicates the path to the Rat King, I need you to first go ahead where the other arrow points. Jump over the wall and you'll find two distressed NPCs—Kevin and Yuri—resting in the corner (see second image above). Talk to the explorers and they'll assign you the Lost Party quest.
Remember the first arrow we talked about recently? Jump back over the wall and go to that spot, which should be on your right. Gather the moss to reveal an opening through which you can slide to enter (first image above). Walk down the narrow passageway and jump over the wall on your right when you see the opening indicated in the second picture. Inside this cave, you'll find The Rat King boss who you can defeat if you've prepared well and have a leveled up character with some good weapons.
For more on Roblox, check out How to get to Lakeshire in Rune Slayer on Pro Game Guides.