As you play the game, you will find that some of the residents in the town of New Nevaeh will have sidequests to give. None of the sidequests are particularly taxing, as they usually just require you to speak with other NPCs, get a specific item, or gather some resources. For this achievement/trophy, you will need to finish all of the sidequests given by residents. These are any NPCs that don’t actually run the shops, as those are considered Shop Quests.
The Bulletin Board in the Plaza will list the quests available at the time, but you will still need to hunt down the NPCs to actually start and finish the quests. Basically, if you fill out all of the Stamp Cards, then this will unlock. There’s the Silver, Gold, Platinum, and Black Cards, totalling up to 160 Stamps once everything is said and done. Note that there are more quests that unlock after filling out the Black Stamp Card, but those are completely optional and you don’t need to do them.