I've searched a bit and can't find a 2010 A6 Service Manual.

I'm sure it exists. How do I get my hands on one?

 

Probably only place where you can get a hand on one is the Audi of America. They will not be selling it to an individual for sure. Wait about a year and Bentley will have it. Keep in mind though... new audi manual from Bentley is broken up in sections and will cost you an arm and a leg, and a kidney.