Eagles demonstrate their prowess in aerial combat by utilizing their speed, agility, and powerful talons to outmaneuver and overpower other birds of prey. They are known for their impressive diving and swooping techniques, which allow them to surprise and outmaneuver their opponents in mid-air battles. Additionally, eagles have sharp eyesight and keen hunting instincts, enabling them to spot and target their prey from great distances, giving them an advantage in aerial combat situations.