Kratos has killed gods that Achilles could never dream of challenging — the power gap between them is enormous.
Achilles is the greatest mortal warrior in Greek mythology. Blessed by the river Styx with near-total invulnerability (minus the famous heel), his speed and combat skill allowed him to single-handedly rout the Trojan army. He killed Hector, the greatest Trojan warrior, and was prophesied as the most dangerous fighter of his age. He's the gold standard for mortal combat excellence.
But Kratos killed the god of war, then killed the rest of the pantheon for good measure. By God of War III, Kratos is overpowering Titans, ripping off Helios's head, and beating Zeus to death with his bare fists. He's not a mortal warrior — he's a divine engine of destruction whose power scales to the beings he fights. Achilles has never faced anything remotely close to what Kratos casually destroys.
The Styx invulnerability is Achilles's best defense, but Kratos has bypassed magical protections before. He broke Baldur's invulnerability curse in God of War (2018) and has killed beings with various forms of immortality and invulnerability. The Blades of Chaos, forged by a god, would almost certainly bypass the Styx's protection. Even if they didn't, Kratos could simply target the heel — he's fought enemies with single weak points before.
Achilles's combat skill is world-class, but Kratos has fought and killed beings with far superior combat abilities. Ares, Baldur, and the Valkyries all possess supernatural combat speed and skill. Achilles, for all his legend, is still a mortal-tier fighter enhanced by divine blessing.
Achilles's Styx invulnerability makes him immune to virtually all physical damage, and his combat speed and skill are the greatest in the mortal world. His divine armor and weapons were forged by Hephaestus himself. If his invulnerability extends to divine weapons, even Kratos would struggle to put him down, buying time for Achilles's superior technique to find openings.
Kratos kills gods. He's overpowered Titans, broken magical invulnerability curses, and his divine weapons are specifically designed to kill immortal beings. The Blades of Chaos would likely bypass Styx protection as divine weapons, and even if they don't, Kratos has the power to exploit the heel weakness. The gap between killing Hector and killing Zeus is astronomical.
Kratos wins decisively. Achilles is the greatest mortal warrior, but Kratos stopped being mortal a long time ago. The Ghost of Sparta fights at a divine tier that Achilles simply cannot reach, and his experience breaking magical protections means even the Styx blessing likely won't save the hero of Troy.
Achilles also fights
Kratos also fights