I found this to be easiest at the start of Dead City. No killing required, just run into the first building on the left and grab the key around the corner. Then head upstairs and unlock the lockbox. Restart checkpoint; rinse and repeat.
Check out the video below for a full playthrough of the game showing all collectibles, miscellaneous achievements like this one, and the Moral Points I obtained (I skipped a lot of them) in order to get the Redemption achievement. The DeadCity mission starts at timestamp
1:50:36 and shows this first lockbox as I run through the mission.