Where are the Achaians at the opening of Homer's Iliad and why did Apollo send “deadly arrows” against them?
Homer's Iliad opens in the Greek camp on the beach near the town of Troy (also called Ilium or Ilion). Troy is located in the northwest corner of what is today the country of Turkey.
At the beginning of the poem, Chryses, a priest of Apollo, comes to the Greek camp with an offer of ransom for his daughter, Chryseis, whom the Greeks have taken captive. Chryseis is now in the possession of Agamemnon, commander-in-chief of the Greek forces. Agamemnon treats Chryses rather rudely and refuses to ransom Chryseis.
Rejected by Agamemnon, Chryses prays to Apollo for assistance and Apollo responds by striking the Greeks with a plague (Iliad 1.50-51):
First, the god massacred mules and swift-running dogs,
then loosed sharp arrows in among the troops themselves.
(Ian Johnston translation)
Thus, Apollo's arrows are blows of illness that afflict the Greek army. This plague eventually prompts Agamemnon to return Chryseis to her father.