Reverse works on level ground, however, if backing up hill will not back. Does this require new trans or some kind of adjustment and/or flush?
Transmission on 2001 Audi A6 Quattro
If the transmission will not operate under the pressure of going up a hill the problem is most likely in the transmission unfortunately. I would first have someone with a scan tool that has Audi diagnostic capabilities plug in a scan tool and see if the transmission has any trouble codes stored. Have the transmission fluid level checked.