For weapon locations, I refer you to TheDustyCactus's solution. But I had a few unanswered questions that I had to find out for myself, so in case anyone else is wondering:
Yes, you must get all the guns in the same playthrough. If you mess up like I did and a district goes hostile before you bit the last citizen who holds a weapon you need, you're SOL. Simply getting that last weapon on a second playthrough won't be sufficient - you need to get ALL the guns again in the new playthrough.
The good double-barreled shotgun can be acquired as early as Chapter 4. As soon as you have access to the West End, you have access to the area where you can pick up that gun. However, you will unfortunately still need to play through the first section of Chapter 5 before you can unlock this achievement, because Edwina is mesmerize level 5 and you need to deal with Dawson in the mission "Unnatural Selection" before you get to that level yourself.
Yes, this CAN be earned while playing in "story mode." Again, in case you missed this on your first run and need to start a fresh one, playing in story mode makes it a bit simpler if you want to speedrun through and just collect weapons. There is still combat, but it's baby mode.