This can be seen in the Set Dungeon screenshot from the Patch 2.4 preview; note the objectives in the cropped view of the shot to the right. Not taking “fatal damage” is a requirement to complete the dungeon, along with killing every Elite with Impale and avoiding all Arcane damage. That’s just the ruleset for that particular DH Shadow’s Mantle set dungeon, but presumably all the other Set Dungeons have the same no death requirement.
Note that it’s not about dying, but taking “fatal damage,” thus all of the passives and items that provide resurrection after taking fatal damage won’t help you complete the challenge. Set Dungeons thus sound a bit like that one timed event in the crumbling tomb, where you die/fail if you don’t find the Treasure Room in time, but it’s not an actual death; you just appear back at the entrance having failed the event.
What do you guys think of that wrinkle? On one hand, dying in Hardcore is supposed to be permanent. On the other hand, everyone is Hardcore in a Set Dungeon, in terms of what must be dome to successfully complete the event, and Set Dungeons work differently than the normal game. They’re kind of mini-games, with different rule sets and they aren’t random but specifically designed in layout and monsters.
Presumably the Set Dungeons are balanced to be very difficult to complete within the time, while avoiding one damage type and using just one specific skill to kill Elites, etc. Thus there’s challenge enough in having to play a specific odd way, and players will probably need to try each one multiple times to do everything just right and earn the achievement.
Debate in comments, and click through for the full size Set Dungeon preview screenshot.
Set Dungeons = Non-Permanent Hardcore Death