The Blue Medallions are part of a minigame within the main game of Resident Evil 4. You first get this assignment by seeing the note pinned up on a tree in the farm, right below a blue medallion. When you reach the Merchant, he asks you if you have seen the Blue Medallions and that if you shoot ten, he'll give you a specialized handgun. If you shoot all fifteen, he will give the gun with a free upgrade in firepower.