You unlock this Achievement as soon as you have found and read 20 magazines. The following trophy will be unlocked:
Read 20 Magazines
Find all Magazines
The trophy and achievement requires you to find and read 20 magazines. It does not have to be 20 different magazines. You can pick one and the same 20 times. To do that, take a magazine and return to the main menu to restart the game. Then the magazine should be spawn again, do it 20 times and the trophy is unlocked.