Bosses are hostile enemies that don't re-spawn after they die. They mainly lie in the borders of the map, except the Mammoth and Disco Duck at the middle. Defeating a boss efficiently will require some food and a few items, but in return they drop good items.
Alligator Men are located in the four corners of the map on individual islands.
The Mammoth is the boss at the middle of the map.
The Hydra will wander around the trade route after being summoned at the Ominous Altar.