There seem to be two camps as far as Arkham City goes... For some, hybrid PhysX works great, for others, it causes an instant BSoD.
I'm in the "instant BSoD" camp, where starting Batman: Arkham City with hardware PhysX enabled instantly dumps me to a BSoD with an Nvidia DLL listed as the cause. Software PhysX runs normally.
A few people have said they had to uninstall and reinstall Nvidia's drivers (and re-run the hybrid physX patch) after installing Arkham City, and that doing so fixed the BSoD issue. I'm going to give that a whirl now.
Recommended Nvidia driver versions for Arkham City:
PhysX System Software: 9.11.0621
Hybrid PhysX: 1.05ff
Thanks for the reply. I'm currently 55% done with the game on normal. I plan to play it again on the harest level when I'm done and I'd like to use the hybrid physX. Please post back and let me know if the uninstall/reinstall worked.