Ok, I've already posted this on the Open Request section of the forum, but it seems someone managed to get the game running on Ubuntu using wine.
Here's his message on WineHQ
Hello Everybody, hope this would help anyone trying to get the game work to its full (MAX Video setting):
First, my config:
OS: Ubuntu 12.04 LTS
video card :Radeon HD 6570/7570 - set up to 1920x1080
Wine 1.7.19 32-BIT Prefix
Then, steps to get everything fine (some of them are taken from your posts, thanks and respect to everybody )
1) "StrictDrawOrdering"="enabled" (as written above)
2) all direct x / D3D packages
3) devenum quartz wmp10 ffdshow
4) quartz library to "builtin, native" instead of "native, builtin"
5) INSTALL WineD3D_Dark_Souls_II_v1.0.tar.bz2 to fix invisible enemies problem
6) If using ATI card (don't know about nvidia), be aware that at first run (after character creation)you should disable Motion blur AND Anti-Aliasing! after first run, you can enable them again... I had same issue with DS.
7) Have fun
I don't know if this will help you, but I hope it does^^