You're trying to cover a huge amount of logistically-complicated ground in a very short period of time. I urge you to reconsider. You can have a much nicer vacation if you don't rush around so much. Apparently you've already booked flights into Italy and out of Athens. That's more than enough for 2 weeks (or 2 months).
Are you sure there's a ferry from Dubrovnik to Budva? This 2017 TripAdvisor thread suggests that there is not. There is bus service between Dubrovnik and Kotor as well as between Kotor and Budva. Whether there's a single bus running that entire route, I don't know. You can explore bus schedules on the BusCroatia website, but definitely verify the information when you get to Dubrovnik, and understand that the Dubrovnik bus station personnel may not be fully informed about what buses do once they cross the Montenegrin border. In all cases, pay attention to the day of the week. Especially on Sundays and holidays, things may go sideways.
Podgorica is the capital of Montenegro and by far the least interesting place I saw when I traveled through the country in 2015. It is not a place I would go on a short trip unless I had to for reasons of transportation.
Kotor has a walkable wall; Budva does not. Kotor gets occasional visits from monster cruise ships; you don't want to be there on the same day. Their historic areas are otherwise superficially similar, and perhaps similar enough to Dubrovnik that you can skip them on this trip without feeling as if you've missed out. I did not go to Dubrovnik on my Montenegro trip, having been there twice previously.
Tivat I haven't been to.
Two other coastal cities I like, which are not as touristy as Kotor and Budva: Herceg-Novi (between Dubrovnik and Kotor) and Ulcinj (farther south than Budva).
I also enjoyed the interior town of Cetinje, and I've read good things about the national parks. The latter pretty much need a car, I believe.
I haven't been to Greece recently enough to comment beyond pointing out that the country is much more than Athens.
