Veteran monsters and stronger versions of the bosses you fight in the story. You can get the maps to fight them by defeating the regular versions of the bosses in their grottos in a certain period of time. Once you receive your first veteran boss map, your navigator will say that it will take him some time to decipher them. You will get actual access to them after you complete the game. You will then get the trophy once you defeat them all. The other optional bosses do not need to be defeated, merely the stronger forms of the story bosses.