The Undying/Immortal achievements in Ulduar have been created on a per-boss basis; that is, you don't have to do the entire instance without anyone dying; you can keep working on the achievement over as many raids as you need to.
The Undying, Part Two has been renamed to "Champion of Ulduar" and now require you to kill each boss without dying, but not necessarily during the same reset Title Reward: Champion of Ulduar.While I do think this "dumbs down" the achievement a little, I really can't get away from the hatred I feel towards the current Immortal achievement. There's just too much random luck involved; too many times that you are put at the mercy of a bad internet connection.
The Immortal, Part Two has been renamed to "Conqueror of Ulduar" and now require you to kill each boss in Heroic difficulty without dying, but not necessarily during the same reset. Title Reward: Conqueror of Ulduar. (Source).
Previously, I would have (sullenly!) sat myself out of a raid rather than risk the title for others. In Ulduar though, it won't matter - because I won't be jeopardising an entire week's work for 24 other people by disconnecting on the final boss; at worst, it would stop them from getting one boss. That's still not good, of course, but it wouldn't be the way it is now - slog your way through the entire instance for several hours, allllllllllmost get the achievement, and then have someone disconnect in a void zone, YAY! This time around, if they disconnect and die, it hasn't ruined the entire week's effort - it just means that there's one last boss to finish off for the achievement.
Some quick notes, as summarised on the WoW forums:
-2nd attempts in the same reset will not count, only first try
-Can be done over multiple resets
-Algalon is not apart of this achievement, which is intentional
-The titles are currently placeholders and should change when the patch hits
-Naxxramas Immortal/Undying will not change, this is for Ulduar only
I'm all for tough achievements and skill and whatnot, but the Naxxramas Immortal is horrible, stressful.. I hate it. The fact that Ulduar is per-boss actually makes me WANT to do it, rather than dreading it - I'm actually looking forward to it now!