Escalating Nightmares are a feature of Diablo IV, introduced in the Sins of the Horadrim update.
In these Nightmares, players complete three consecutive dungeons. On Torment difficulties, monsters become stronger with each consecutive dungeon. Two additional affixes are added to each consecutive dungeon. If all three are completed, the player gains access to Astaroth's Lair, where they confront Astaroth himself.