Cottus is one of the three Hekatoncheires, a hundred-handed primordial son of Gaea. He has lived for thousands of years beneath Themyscira, until summoned by Alkyone to deal with Wonder Woman. Both Alkyone and Cottus claimed that Cottus is Diana's father, that the clay Hippolyta used to create Diana was taken from him. This filled him with rage for eons.
Now that Alkyone has summoned him, he engaged Wonder Woman wanting what was taken from him back. But Diana, helped by the Amazons and Thalarions, and the megalodons of Themyscira, rejected the demon and used the lightning of Zeus which coursed through her bracelets to electrocute him. Whether he is dead, or simply returned to the depths he calls home, is unknown.
Diana encountered him once before, during the "Challenge of the Gods" story arc. When she entered Doom's Doorway beneath Themyscira, she saw a bullet casing lying on what seemed to be a staircase, but was -- in fact -- Cottus' spine. Diana ended up breaking his spine when he attacked her, and the assumption was that he was dead. Prior to Diana's birth, Diana Trevor had crashed on Themyscira, found the Amazons engaged in battle with Cottus at Doom's Doorway, and entered the fray to help defend the Amazons, only to meet her end when the son of Gaea crushed her skull, but not before Diana Trevor shot Cottus, presumably wounding him. This enabled the Amazons to escape from Doom's Doorway, making Diana Trevor an Amazon hero.