What are the different chests I can receive in the Soul Box?

What are the different chests I can receive in the Soul Box? - Crop unrecognizable tattooed painter spraying blue paint from can on multicolored wall with creative graffiti while standing on street in city

Running through the game a second time, skipping many of the side quests, I've noticed a few things I missed my first time around. One of the more major things I've noticed is that the chests made available to me in the Soul Box in route C/D were different. I seem to recall getting more than I got this time. This is reinforced by the fact that there was a voice commending me for various things and telling me I was being rewarded for them.

If there are, indeed, different rewards in the Soul Box, what are they and what are they for?






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Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.

Images: Felicity Tai, Felicity Tai, Andrea Piacquadio, Mathias Reding