The climax in the story "Leiningen Versus the Ants" comes at the end, as Leiningen strives to close the river gates and wash away the attacking horde of ants:

Then he was at the weir and gripping the ant-hulled wheel. Hardly had he seized it when a horde of infuriated ants flowed over his hands, arms and shoulders. He started the wheel -- before it turned once on its axis the swarm covered his face. Leiningen strained like a madman, his lips pressed tight; if he opened them to draw breath....
(Stephenson, "Leiningen Versus the Ants," classicshorts.com)

Leiningen has fought back the ants on all fronts, but their numbers are overcoming his ability to defend. The climax covers this section of the story, as Leiningen's struggle against the ants becomes personal and personally harmful, instead of separated and directorial. In a last-ditch effort to destroy them, he puts on protective gear and runs for the river dam, which will also destroy his crops, but leave his plantation mostly intact while washing the ants away. As he runs through the ants, Leiningen is bitten and stung, and hurt very badly, but manages at the last moment to dam the river and defeat the ants.