He set out on a journey to defeat his sworn enemy.
仇敵 stresses deep personal hatred toward an enemy, while 宿敵 stresses the long, ongoing history of the rivalry.
Compound of 仇 (kyū, 'enemy, grudge') and 敵 (teki, 'enemy'). The exact historical derivation is uncertain, but the combination reinforces the meaning of a bitter foe.