One place I would start would be to check the dc amp flow with the battery charged and eveything turned off. Use a multi meter and measure dc amp from the positive terminal to ground. Although there is dc voltage from positive to negative, there shouldn't be any current draw unless something is "on", i.e. if nothing is drawing down the battery, current flow should be 0.
If something is drawing the battery down, amount of dc amp might hlep isolate what it might be.
If there is current flowing, you might also consider pulling the fuses in the fuse block one at a time and see if a particular fuse / circuit is the culprit. If the problem is isolated in one electrical circuit, pulling the fuse for that circuit should stop the current flow. Then you would at least have further information as to which circuit in the car's electrical system is problematic. You would have to further isolate components within the circuit to find the exact location(s) of the problem.
By the way, any mechanic who:
1. charges you for a new alternator
2. charges you for a new battery
3. doesn't fix the problem
4. has the audacity to tell you he doesn't have time to work on your car
doesn't have a clue in the first place as to what is wrong or what he is doing. He is simply guessing at your expense. He is also looking for an excuse not to work on your car without coming out and telling you that he shouldn't work on your car because he doesn't have a clue. Definitely find someone who has better skills and business ethics.