Rodan! The Flying Monster!.

Rodan follows in the footsteps of other Japanese monster movies, such as Godzilla, which involve a giant monster being awoken from an ancient hibernation by human beings. In Rodan, miners digging far into the earth stumble across a clutch of giant, prehistoric insects called Meganulon, which viciously attack several of the miners and prompt a government investigation into the matter in the year 1957. The giant bugs turn out to be little more than food for two gigantic flying beasts called Rodans, similar to pteranodons but far larger and more powerful, who hatch from giant eggs and proceed to terrorize the entire world.

In my opinion this is pretty cool but I wish Rodan would battle another monster