Brass Balls achievement guide (Bioshock, German game version):
1) Download the proper Title update ("Ryan Industries Plasmids and Gene Tonics") DLC from Marketplace;
2) Choose: Disable Vita-Chambers: On in options menu as fast as possible - if you don't do that and if you die spawning in Vita-Chamber you will NOT get the achievement even if you load game which was saved before spawning - so it is much safer to disable it at all
3) You can also get this achievement if you didn't download the DLC at all and completed the game on Hard difficulty without using Vita-Chambers (only manually loading the game from the proper save). Then:
a) download the DLC
b) load the saved game just before the Atlas (last boss) fight
c) kill Atlas
Achievement should pop during the final cut scene.
I'd like also add something what is not confirmed, but might be true, because I heard that people have problem with this achievement even if they do everything well.
I think that the most important thing to get this achievement is to download the proper Title update DLC to proper copy of the game.
It means that you have to download update from German Xbox Live Marketplace to use it with German version of the game (even if the game is in English language).
That might be the reason why I didn't unlocked this achievement - I downloaded DLC from UK account and used with German copy of the game.
I also completed Bioshock for the second time (including Brass Balls) using most popular European version without any issues (with DLC downloaded from UK account).