Easy Method to Farming Battle-Tested Weapons - Octopath Traveler
It is best to use the 1HP Last Stand Apothecary build for defeating these citizens. It should be able to one-shot most of them depend on your equipment loadout.
I have received these weapons in as little as 3 tries, and at most 80. It's all random so just keep on grinding them. Best ones in my opinion to farm for are the Blade, Axe, Bow, Staff, and the Robe.
For single zone areas such as S'warkii or Atlasdam, you can just fast travel between two locations, or use a savepoint.
For areas such as Bolderfall in which you have to load a different part of the area, it's best to beat the person guarding the house then take the staircases to the north area. Exit the game and load up the autosave file, it will put you in the lower part of the map with the door person already defeated.
I mis-worded (is that even a word) the part about obtaining it after certain quest. It can actually be farmed as soon as you get Olberic or H'annit, just be prepared for a long fight if you chose to do so then. You can obtain one of each by purchasing them from others after certain quest. It's been to long since then, not even sure how to get those anymore, but they can always be farmed.