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