Throughout the game there are many occasions where you can engage in conversations with allies or objects in the world. There are 37 of these in total that count towards this trophy. There are actually more of these conversation pop ups that you will run across in the game, but aside from the 37 required ones, these do not count towards the trophy. Note that there are a couple of "conversation prompts" where a conversation icon won't appear to notify you (eg. the darts). You will still however need to interact and trigger these conversations as they count towards the trophy.
You will know an optional conversation can be triggered when a prompt appears overhead your allies.
It can seem confusing at first but luckily for you the complete list of the conversations that count towards this trophy can be found here (Credits to Wozamil):
Here's a video guide with all 37 optional conversations: http://www.youtube.com/watch?v=gk1M3dr7OjM
The game has a lot more conversations than that, but most are irrelevant for this trophy. After listening to a conversation it will be saved automatically (no need to reach the next checkpoint). You can still get missing conversations after the story via chapter select.
There is no way to see which conversations you have already completed. So make sure to do them in correct order! In the statistics section of the bonus menu you can only keep track of how many you have in total. Once it shows 37 conversations you should get the trophy.
Watch out. I got this only on my third playthrough because I didn't realize there are two prompts in the room with the dead bodies when you're with Dave in Winter. After running down the bridge and entering the room (with a Bloater, eventually) you'll see two bodies. You need to push Triangle on both of them
@#1 Powerpix I love your guides and I am subscribe on YouTube. But I notice I am missing some conversations and don't know which one so I am doing it on Survivor and using your guide.I notice before #20 you go up the ladder there are DEAD Soldiers on the ground near the "Death To Freedom" tagged on the wall I got one of those ICONS for a conversation with Ellie.Still no trophy but will go through see what I missed.
I just want to reassure everyone that if your stuck on 36/37, it's not glitched. Either A, you missed one, or B. One didn't register. I chapter selected and went through them all on update 1.03. Conversation 9 was the one that popped for me. I remember doing it, but it must not of registered.