A Region Boss is a monster with the below-listed massive list of buffs. Although they are denoted with a special icon in the game, they are not actually a different monster; as with all title variants, the region boss will be one of the monsters normally found in that area.
The region boss fight does differ from normal monster fights in one key way: you will fight the same region boss until the boss dies. The region boss will keep the same HP from the previous fight and also maintain any debuffs you put on them. This lasts until you kill them (at which point another random region boss will 'spawn') or you leave the region. Leaving and returning to the region is also a way you can reset the fight intentionally in order to go up against a particular monster that you have an edge against, either to attempt a one-shot or to kill them in as few encounters as possible.
Initiating a rebirth does not reset the Region Boss. (Confirmed)
Killing a region boss has a chance to drop a Pet, and, as with all titled monsters, it has a much higher chance of dropping higher tier equipment.
-Cri. mul + 50
-Cri. mul x1.5