You may have noticed that symbols may appear above a monster's level. There are three symbols:

Feather: Indicates that it is flying and can only be attacked by other flying monsters. It also can fly over other monsters, but unfortunately, other monsters can move under it. Monsters with this symbol use double the movement cost.

Tunnel: Indicates that it digs underground to move around, so it can move past other monsters.
Arrow: Indicates that this monster can attack a flying monster.