An interesting question. My short answer is, "With difficulty." To expand on that, they are such different men in such different cultures and circumstances that it is tough to make useful comparisons. Both are major figures in their realms. Both are skilled warriors. Both are intelligent. Both are proud, and both are close to their fathers. Both delay crucial violence. Beyond that, however…it's hard to say. Hamlet is forever divided and in his head. Achilles, by contrast, is driven by emotion. Hamlet wants to be absolutely right before he acts. Achilles acts, and trusts his actions to be right. Hamlet seems fond of Ophelia, but his ego is not bound to hers. By contrast, Achilles doesn't seem fond of any woman, but his ego is bound to them as his prize.