Which river in Troy did Achilles fight against in person?

The river Achilles fought against in person at Troy was the Scamander.

The Scamander flowed from Mount Ida across the Trojan plain and joined the Hellespont north of the city. In Homer’s Iliad, the Greek camp stood near its mouth, making the river and its surrounding plain a major setting for the battles between the Achaeans and Trojans.

During the fighting, Achilles angered Scamander by killing so many Trojans that their bodies choked the river. Homer presents the river as a personified deity who confronted Achilles directly, sending floodwaters against him and nearly drowning him. Hera intervened by having Hephaestus use fire to force the river back.

The Simois was another river near Troy and a frequent companion of the Scamander, so it is an understandable distractor. The Styx, by contrast, belonged to the underworld; it was associated with Achilles in a later invulnerability legend, not with his battlefield struggle at Troy.