To enter the Palace of Paroxysmus you must have an Acid Proof Rope in your backpack. This item can be crafted by Carpenters who have learned the recipe, or it can be bought from the NPC who can be found outsiode the dungeon.

To gain access to the peerless boss, Chief Paroxysmus, you must gather a number of items from the monsters in the dungeon and drop them in the cauldron found at the large lake of acid. This will result in a number of teleport items that will take you to the peerless area.