You can just pop the FOB open with a coin and the battery can be purchased at your local drug store. The battery is a 2032.
2015 A6 TDI Prestige with 19" Sports Package with Season Dedicated Tires - Oolong Gray Metalic, Nougat Brown Interior, Dark Brown Walnut Inlays, Black Headliner, Driver Assistance Package, Cold Weather Package, Night Vision Assistant with Pedestrian Detection.
RIP - 2005 A6 4.2 - (February 2005 - August 2014) (142,000 miles)
C6 TSB Library link (Thanks to Dr. Cold for his help in setting this up) http://uberlame.com/a6_tsb/