Audi Repair Questions? Ask a Mechanic for Answers ASAP
What do you mean "flailing"? Do the revs shoot high, like it is slipping or not engaging either gear at this time?
Does your PRNDL display on the dash show normal? Have you ever had it scanned for faults? It sounds like the solenoid that drops pressure between shifts is "out of sync" with the shifting, or maybe the plates in the clutch pack for 3rd are sticking. If you've never had a fluid change on your tranny, I would do so, including dropping the pan and changing the filter. At that time you can see if there is any metal flake or other particles in the pan that would indicate breakdown of clutch discs.
It should be about 4.5-5 quarts, but be aware that a special synthetic fluid is needed for VAG vehicles. And I bet you probably don't have a dipstick on this, it should have a fill port that requires it to be filled through the bottom with a gravity filler or a pressure tank.