If you knockdown all enemies and negotiate with them, this should come quite quickly over the course of the game. The tough part, and the part most likely to discourage people, is the actual negotiating.
The key are the tips in the in-game tutorial/help section. If you ever forget, you can look it up there, but for ease of accessess, here it is. When you hold up an enemy, look above their name to see their demeanor, and then use the table below to tty to figrure out the right answer (sometimes it isn't easy).
Gloomy shadows like vague answers, and dislike serious or funny ones.
Irritable shadows like serious answers, but not vague or kind ones.
Timid shadows like kind answers, but not vague or funny ones.
Upbeat shadows like funny answerd, but not serious or vague ones.
This should make aquiring new personas much easier. Even if you're fully stocked on personas, acquiring it and then choosing that persona as the one to let go still counts it to your compendium and for this trophy.