This two-headed fearsome creature is a Chimaera, a fire-breathing monster that combines elements of a lion, a snake, and a goat.
In this scene, Greek hero Bellerophon stabs the monster from underneath as Pegasos strikes its face. Teamwork.
Wine Cup with Bellerophon Fighting the Chimaera, about 565 B.C., Attributed to the Boreads Painter. J. Paul Getty Museum.