The best way to work on this trophy is to simply complete the main story, since you will earn at least thirty-five audio logs just from that; therefore, you don't need to go out of your way to collect every single audio log that will pop up on your map.

The audio logs are depicted as the speaker symbol on your map, and will appear there when you are physically close to one. For further detail on how go around collecting them, see "Collectibles And Tech Points" in the Tips & Strategies section.