CONTAINS SPOILERS

Here's what to do if you encounter a Kodama with red eyes wearing a skull helmet and holding a wand. Greet it and "it seems as though it wants something" pops up on the screen. Go to your Equipment or Items tab from the menu an pick any item you're willing give away (weapons, armor, consumables, etc.). Select the Drop Item option. The Kodama will pick up the item and gift you a bunch loot.