This is an unmarked secret quest that is available through the Darkening of Tristam event.
Starting the Quest
Enter the Anniversary Dungeon, the Labyrinth, and make your way down to Level 9. Search the area to find the Black Mushroom. These can appear anywhere on the dungeon floor, so search it thoroughly. Interact with it to get the Rotten Mushroom. With it in hand, exit the anniversary dungeon and head back to Tristram.
Head out of town to the Northeast. Take the First turn to the Southeast. This will lead you to Adria's Hut.
LEAVE THE COW CORPSES TO THE RIGHT OF THE HUT ALONE. ELSE YOU WILL NEED TO START A NEW GAME TO COMPLETE THIS ACHIEVEMENT.
Inside it is the Cauldron. Head over to it and interact with it.
Once back in town, it is time to revive a few people. Head to the Southwestern corner of town. You will want to find Farnham's Corpse. Interact with it. As long as you have the Witch's Brew then Farnham's Ghost will appear and drop Drunkard's Debt.
Return to the Old Ruins and enter the portal to Tristram. Once there, return to Adria's Hut Tristram. To the right of it you will see 3 Dead Cow. Interact with them in this order: Middle (2), Left (1), Right (3).
Done properly, a new area will open to the right of the hut: Abandoned Farmstead. Head into it to reach the final part of this quest.