The ants first attack—and then consume—the eyes of their victim so it will be blinded. They also bite wherever flesh is exposed because they can inject their poison into the victim.

During the war between Leiningen and the "act of God," one peon strikes at a clump of ants with his spade, but does not pull it back quickly enough, and the ants swarm up the wooden haft. Unfortunately, he does not drop it in time before the ants are upon him.

They lost no time; wherever they encountered bare flesh they bit deeply; a few, bigger than the rest, carried in their hindquarters a sting which injected a burning and paralyzing venom.

Later, Leiningen sees a pampas stag that is covered by ants. "As usual they had attacked its eye first." Witnessing this poor, tortured animal causes Leiningen to imagine what could easily be his fate, too. He wonders if he should have listened to the official, and if, in his inflated pride, he may have taken on more this time than he can manage.

What part of the victim do the ants always attack first in "Leiningen Versus the Ants"?  

The thrilling short story "Leiningen Versus the Ants" by Carl Stephenson tells of an attack on a plantation in the rainforest of Brazil by an army of large ferocious ants. The owner of the plantation, Leiningen, decides to take a stand against the overwhelming swarm instead of flee. He devises defenses comprised of moats filled with water and with burning petrol, but the ants continue to advance until he floods the plantation by damming the main river.

The descriptions of the ants swarming over and devouring their prey are horrifying. In one instance, a pampas stag has become covered in ants and collapses on the far side of a moat from Leiningen.

It had strayed near the zone of the army. As usual, they had attacked its eyes first. Blinded, it had reeled in the madness of hideous torment straight into the ranks of its persecutors, and now the beast swayed to and fro in its death agony.

From this passage, we can see that the ants usually attack the eyes first. However, in an earlier passage, when the ants swarm up a shovel and attack one of the plantation workers, they do not go straight for the eyes. Instead, the story says that "wherever they encountered bare flesh they bit deeply."

We can see from these passages that when the ants attack they usually, although not always, go for the eyes. Sometimes they simply bite whatever bare flesh they can grasp.