Agamemnon's name is mentioned only once, and we have to infer a lot based on the stuff that's going on around him. He appears to be fighting the Minotaur when we first see him—something that Theseus should be doing, not Agamemnon—while the Trojan War, where he actually appears in legend, is long over. So, we need to do a little detective work to figure out who he is, though once we do, he gets very, very interesting.
On the surface, Agamemnon is everything you'd want a father figure to be. He's brave and kind and wise and strong, and he treats Kevin like an equal. He's clearly quite keen to keep the boy, too. Had the dwarves not snatched Kevin away again, he would have made Kevin his heir:
AGAMEMNON: I have decreed that this boy shall remain here with us in our city. Furthermore, he shall from this day forward be my own son, and heir to the throne of Mycenae.
That's a pretty awesome deal for a kid whose real father is more interested in the latest toaster than anything Kevin has to say. Agamemnon represents the great promise of Kevin's adventure: the chance to find someone who loves him, who gets where he's coming from, and who wants to spend as much time as possible with him.
But there's a darker side to it all, and we only see it from hints out of the corners in the film. Gilliam and his team didn't need to make this dude Agamemnon, after all. He could have been Theseus or Perseus or any other Greek hero, and the arc of the story wouldn't have changed at all. But they went with Agamemnon...and there's a very specific reason why.
If you notice, this dude is not on the best of terms with his queen, Clytemnestra, who spends every scene she's in giving the man a serious skunk eye. She doesn't like him, and if you know your Trojan War stories, the reasons become obvious. Before setting out for Troy, Agamemnon earned himself a bucketful of wrath from the goddess Artemis. In order to get her off of his back, he had to sacrifice his daughter to her.
That's hardcore, folks. And don't think Clytemnestra didn't forget it. In fact, in mythology, shortly after Agamemnon returns from Troy, she totally axes him to death in his bath—and that's likely where he's headed shortly after the dwarves take their leave. Now think about it: if she's cranky enough to kill him for sacrificing their child, how angry is she going to be when he shows up with a whole new kid? And then claims the kid is going to inherit the throne?
The dwarves probably spared Kevin a messy death, and while Agamemnon is the perfect dad for him, his less-than-perfect-dad status is clearly going to come back to bite him.
If you want the formal rundown on Agamemnon's mythic history, Shmoop has the hookup, as always.