Find this skull in the "It's Your Own Fault" shrine, after doing the main quest in Act 2, Chapter 5 called "Let the Waters Flow." This is in the sewers of Moresby. Find the two green barrels near a dead end, after entering near the church. Turn left, going through some fogged rooms, making sure to keep to the left. Go to the dark section of the tunnels, which is through a gated entrance, then take the first right. There should be a ladder on your right in the room with graffiti and upper catwalk. Climb it and you should find the Purple Skull at a candle lit shrine at the end of the catwalk. You deposit the Purple Skull in the abandoned house that is made available during the "Uninvited Guests" sidequest in Moresby. Use the stove in the room adjacent to the one with Alicia Jacobs. Your reward is the Mindblowing Military Knife recipe.