I've only gotten the guaranteed DS to spawn once in
this game. This shows that it doesn't have to be a standard game, (this one was AoMC) and it doesn't have to be completely damageless. (I had taken some damage by the time I reached UC) As Appuru said, it can't be done in AoOC, (I made an attempt at it and managed to clear Hell 1 and UC damageless and still only got the Longinus Spear) but I don't think you have to have Conqueror by that point to get it. (In the above-mentioned mortem, I failed to clear one of the levels, and I think it was Halls of Carnage that I missed, since that's the only one listed in the mortem that doesn't explicitly state that I cleared it)
Also I think that DS is more likely to spawn in one Arch100 game that in seven Ao100 games because any unique may can be generated only one time per game.
Hopefully, I'm about to find out, because I'm playing an AAo666 game right now. :) I have a new theory about how to pick it up, so I hope to get the chance to try it. :)