"These hunters are curious creatures. Bloodthirsty and violent to others, they employ a surprising degree of care in raising their young. Every egg is guarded with vigilance, and the hunters will frequently circle overhead to keep watch on their nests. Those who intrude upon them are most unwise..."— Archangel Tyrael(src)
Hunters use the same attack pattern as Demonic Hellflyers: they swoop down from the sky, and can be killed mid-air. Once landed, they cannot lift off again.
In combat, they rely on melee strikes with their claws, and actively pursue their foes.
They are often found circling around the battlefield, waiting for a good moment to land next to their victim. They always land (often in large numbers) if player touches their nests.