To get the trophy that's called "Thanks, old friend.", you will need to speak with Alfred and hear just about everything he has to offer.
To accomplish this goal, I recommend starting a new play through. This way, it will be fresh and new and the game will have an easier time keeping track of what Alfred has said to Batman/Bruce Wayne so far.
As you go through the storyline, you will be completing a lot of main missions and side quests. After you complete one of either, always fast-travel back to the Batcave and hear what he has to say. He will always say something different to Batman/Bruce Wayne. So it's really just a matter of going back and forth from each mission and speaking with him until the trophy unlocks.
He spawns at several points inside the Batcave, so if you have trouble locating him, use Detective mode to scan your surroundings until you see him. He can either be on top level, near the platform next to the Batwing, standing next to the computer that has Detective program on, or on the lower-level platform nearing the training grounds, as he is standing on the edge and looking up.
I also recommend talking to him constantly, for he does give you Alfred's wisdom in the form of experience points, so if you need more exp or have nearly enough for a level, now's the time to do it.
Talk to him after every mission and the trophy will eventually unlock.
Have fun and good luck!