As you explore the various worlds in the game, you will run into and do battle with plenty of enemies. Not only are they important for the obvious reasons, such as giving experience and G, they also drop items that are necessary to unlock new items in the Weapons Shop.
Every normal monster you encounter in the game will be listed in the Monster List section of the Notice Board on your ship. Note that bosses and special enemies are not listed here, and only limited information is available. Once you get the Ultimate Analyze ability, you can press R1 in battles, press Start on any of the monsters and then Square to cycle through various stats, which includes Moe Affinities.
As you will see, most normal monsters have an item that they drop, as well as a second item that can be random (tends to be low level equipment). They also drop Shampurus as well, with most enemies having a common one, as well as a rare one. They also might have an item they drop if you use Captivate on them and turn them into an item.