This guide will tell you how to complete the burning curiosity quest in Xenoblade Chronicles 3.
You will need to farm the Bushwacker ferret by going to the Pentelas region, as shown on the map.
There is a named monster 50 or something, who is dropping all the things you need. As you need purple items, you have to farm him a quite bit, this is easy you just need to beat him down and pop him up, keep doing this again and again until you get your desired items. It will guide you to complete the quest as soon as possible.