Kratos must first completely remove its armor, which can only be done with more powerful attacks like the Phoenix Plume, Rage of Tartarus or by using the Gauntlet of Zeus, before he can actually hurt the monster itself. After weakening them, he can then kill them the same way he does the standard Cyclops, by climbing up and sticking one of his blades into its eye and stomping on the blade. These monsters are encountered in both the depths of Tartarus and the Temple of Persephone.
Also appearing in Ghost of Sparta, their armor can only be destroyed by using Thera's Bane. Once the armor is destroyed, Kratos can again kill them the same way he would kill a normal Cyclops.