Achillies murders his way through soldiers on the beach, taking them on two and three at a time, casually and effortlessly.
Hector is a guy who fights his way through pitched battles, killing all before him - he's the best fighter Troy has to offer and it shows, not just in presentation. He gets into a fight with Patroclus, Patroclus being a guy who is also good enough to kill his way through pitched battles. Hector rather cleanly beats Patroclus.
This also shows how good Hector is.
Achilles toys with Hector, completely overwhelming him at times and not killing him because - as noted in the movie - he's creating a spectacle. He then decides he's finished and pretty much insta-murders Hector (with his own weapon, after yoinking it from him).
Other feats? He beheads a bronze statue with a single swing of his Xiphos - this is not exactly a big, heavy sword. It's a short one.
He also throws that same sword at someone standing about 8' from him. The thrown sword cuts through a metal helmet and cleaves partway through his target's skull. But it doesn't land point-first, spearing in, which would be BS but at least vaguely believable. No, it hits the guy's head edge-on, sideways, and still cuts through the helmet into his skull. <-- this is absolutely nutso, don't know why they went with it other than 'horrific visual', but that's the feat.
Another post by myself going into things about the beach and the Hector fight, for further detail.