There are seven VHS tapes in the game, all found within the house. Simply pick up one of them, and the achievement will pop! You will also unlock this achievement as part of getting the "Dwayne's memento master" achievement.
This achievement is unlikely to miss, but just in case: Simply pick up any one of the VHS tapes and take it with you.
List of all VHS tapes and their locations
Pride: After completing Lucy's chapter, it will be in the toilet in the bathroom.
Negligence: After completing Dolores' chapter, it will be on the floor together with a bit of rope, in front of the door out of the bedroom.
Prison: After completing Rakan's chapter, you will have to drop down through a hole in the floor. Once you land, the VHS tape will be on the floor by your feet.
Addiction: In the basement, near the TV room. Find the board that reads "basement rules", and look in the lower drawer of the stand beneath it to find the tape.
Greed: In the basement, go to the boiler room. You'll find the VHS tape on top of a cardboard box immediately to the right of the boiler.
Indifference: There is a stairway down to the basement between the kitchen and the entrance hallway. At the top of these stairs is a white stand. The VHS will be inside its top drawer.
Affliction: This VHS is found in the leftmost cabinet in the large, open living room where you talk with Rose on the phone at the beginning of the game. (Might not spawn until after you've completed a chapter.)