Batman's tactical genius and modern technology give him the tools to exploit Achilles' singular weakness.
Achilles is the greatest warrior of the ancient world โ blessed by the gods with near-total invulnerability after being dipped in the River Styx. He killed Hector, the champion of Troy, and led the Myrmidons through a decade of warfare without suffering a single defeat. His combat skill with spear and sword is unmatched in Greek mythology, and his divine armor was forged by Hephaestus himself.
Batman, however, is the ultimate problem solver. His entire methodology revolves around finding and exploiting weaknesses, and Achilles has the most famous weakness in all of mythology โ his heel. With even basic research, Batman would know exactly where to target, and his arsenal of batarangs, grappling hooks, and gadgets gives him precision striking capabilities far beyond anything in the ancient world.
In a straight sword fight with no prep, Achilles would be formidable. His divine blessing makes him nearly impossible to injure through conventional means, and his combat skill with melee weapons exceeds anything Batman faces from normal opponents. But Batman regularly fights opponents who outclass him physically and still wins through preparation and tactical thinking.
The key question is whether Batman's Kevlar-reinforced suit and modern combat training can withstand Achilles' bronze-age weapons long enough for Batman to identify and exploit the heel. Given Batman's track record against physically superior opponents, the answer is almost certainly yes.
Achilles is virtually invulnerable everywhere except his heel, making him nearly impossible to damage through conventional attacks. His combat skill is divine-tier, having killed every champion he faced in the Trojan War. His spear and sword technique are backed by superhuman strength and speed granted by his demigod heritage. In a straight melee fight, he has centuries of legendary warriors to his credit.
Batman's entire fighting philosophy is built on exploiting weaknesses, and Achilles has the most famous weakness in mythology. His gadgets provide ranged precision that ancient warriors never faced, his armor can withstand sword strikes, and his combat training spans every martial art. Batman has defeated beings far more powerful than Achilles by finding their vulnerabilities.
Batman wins with prep time, which is his default state. Achilles' heel vulnerability is literally the most well-known weakness in Western mythology, and Batman is the greatest weakness-exploiter in comics. A well-placed batarang or tripwire ends this fight. Without any prep or knowledge, Achilles' invulnerability makes this much harder, but Batman adapts mid-fight better than anyone.
Achilles also fights
Batman also fights