There is not a general formula for what constitutes a monster in Greek mythology. But there are basic guidelines for determining what is a monster and what is not.
Monsters are usually vicious creatures that devour humans and wreak havoc with their lives.
Sometimes they are used by the gods for their various purposes. Monsters can be used to discipline a society, keep them in check, to scare people, or to decimate or destroy an entire populated area. Monsters also may be used to keep people away from a specific area or object. Monsters usually are grotesque in appearance, with features that most humans would find fearful. Monsters are meant so scare people, so that those who defeat them are seen in a greater, more heroic light.