Good morning... sorry to hear about your woes. There could be multiple causes of the issue. I have rebuild my A4LD before, and believe that you have the next gen 4R or 5R transmission. The reverse band has no adjustment, and is actuated by a servo in the valve body. First thing to check is the manual linkage to ensure that the gear shift is adjusted properly. If it is out of sync, the transmission isn't diverting the pressure right to engage the gear. There are plenty of writeups on the proper adjustment.
If that isn't the problem, I would drop the pan and inspect the valve body to see if the separator plate and gasket appear to have leaks, the bolts are torqued to spec, and check if the cover of the reverse servo gasket is leaking. Might be as easy as replacing the gaskets, filter and re-tightening the valve body and servo cover to spec. See if you can get the atsg manual for the transmission to refer to. Depending on your mileage, you might want to also do a valve body rebuild too to ensure that all the valves move freely and remove the reverse servo piston to inspect for a leak in the seals and make sure that the piston isn't damaged and that the apply pin isn't worn. It needs enough movement to fully engage the band.
If none of the above work, then it could be a worn band or clutch, which would require a rebuild unfortunately. Hopefully some other members will pitch in their advise too.
Please let us know what you end up doing and good luck!!!