You can go for this achievement during the Dolores chapter, or any time after completing it, but it's much easier to do it afterwards so no doors are blocked off.
Near the beginning of the game, you will have received a phone call from your elderly neighbor, Rose. The phone is located in the living room near the stairs leading to the progress room.
From there, you should be able to collect the first two pages.
1. On the floor right next to the front door of the house.
2. Downstairs in a walkway room that connects the basement to the garage. The page is in a white drawer.
(To get here, go down towards the basement from the main staircase, turn around at the lamp, walk out the door and straight into this room)
After collecting the first two pages, return to the phone for another call from Rose. This spawns the last two pages.
3. On the floor in front of the TV on the main floor.
4. Upstairs in the closet that connects the parent and daughter's room.
At this point, the achievement should unlock! But I highly recommend that you go to the boy's room to read the comic on the desk. And after reading the book, you can return to the phone for one more pleasant call from Rose.