Here is the full list of all 16 MONSTER X achievements.
Beat Mech Ash Dragon
Beat Metal Garwolf
Beat Thunder Tyrannosaurus
Beat Hunt Mantis
Beat Thunder Bird
Beat Tree Mantis
Beat Flame Tyrannosaurus
Beat Violent Garwolf
Beat Mech Mantis
Beat Bmob Bird
Beat Tyrannosaurus
Beat Mantis
Beat Garwolf
Beat Venom Bird
Beat Flame Bird
Beat Vine