Cursed Archers are more powerful versions of the standard Undead Archers.
They are more armored, and are also more skilled in combat. The fiery arrows they shoot also give off a small explosion that can harm Kratos if they don't directly hit him. In God of War Kratos encounters these foes towards the end of his journey through Athens and in Pandora's Temple. In God of War II, these enemies are encountered upon the Lair of Typhon, and various spots throughout the Island of Creation.
Kratos can kill these foes the same way he kills the standard Undead Archers.