Collector Achievement in Octopath Traveler

This achievement requires that you have had one copy of every item in the game in your inventory at some point. You do NOT have to have all of them at the same time. In fact, it is impossible to do so as some of the items are only given once and used as part of the story (side-quests). You will get the majority of the items by completing the rest of the achievements (quest rewards, inside chests, etc). You'll also need the accessory from Galdera. From there, make sure you purchase one of every item from every town shop, and purchase/steal every item from every NPC you can find.
 

There are some unique items that can only be received by using Challenge/Provoke with Olberic/H'aanit, and some unique items that can only be received via loot or stealing during battle from specific enemies. Check this guide for a list of every item in the game, and how to obtain some of the ones you may not come across naturally.