Final answer:
Achilles is motivated by revenge for Patroclus in his battle with Hector.
Step-by-step explanation:
Achilles is motivated by revenge for Patroclus in his battle with Hector. When Hector kills Patroclus, Achilles is consumed with anger and seeks vengeance against Hector. This is evident in Book XXII of the Iliad, where Achilles relentlessly pursues Hector, ultimately killing him to avenge his fallen comrade. Revenge becomes the driving force behind Achilles' actions in his battle with Hector.