Vigor moves back and forth across the arena. He has four attacks - he will charge the player, often changing his speed while doing so, he will call on the crowd to bombard the player with fruit, he will throw his spear forward, and he will throw his boomerang which arcs out and flies back to him. His attacks are all telegraphed and easily avoided - when he turns to the crowd and they cheer, they're about to throw things; when he stops and runs in place, he's about to charge; and when he stops and raises his arm, he's about to throw one of his weapons. In short, when Vigor stops moving, expect an incoming attack.
Vigor is virtually impenetrable when attacked from the front; his chariot will absorb the blow and he'll take very little damage. The key is to attack him from behind, where he takes proper damage. A charged Horn Spear is optimal for this, as it is difficult to get close to Vigor to strike with melee blows with how he constantly moves about. As long as the player can get behind him quickly enough to throw their spear before he runs off out of hit range, the player should not have much trouble.
After Vigor is defeated, the player receives 1,050 experience points, 1,000 jewels, and the best prize of all, the Gladiator Sword.