I kind of found this by mistake. I had a checkpoint glitch right away so I was forced to quit the game and start over and that's when I saw that collecting the same journal made my achievement progress bar move up another 10%.
At the start of the expansion you will find yourself in the hub. In the room with the very first weapons locker (where you can swap out your 2 guns) you will see a woman at a desk and a journal on the bottom right corner of the desk as soon as you walk in.
After grabbing the journal you can then continue through the recently opened door and meet up with Parrish. After this convo you will trigger a checkpoint when it's time for you to defend the base. This is the moment where you can safely quit to the main menu, select new game, select Beyond The Walls and then choose your difficulty. From here you can simply rinse and repeat in order to collect the remaining 10 journals.
I ended up finishing the DLC with 70% progress after my first and only playthrough by finding 6 of them naturally and collecting the first one after being forced to start over. After the end credits I collected the first journal 3 more times and turned off the game as soon as the achievement unlocked.