The list of supplies for the Slayer helm includes the reinforced goggles, which you can get free during the quest 'A Porcine of Interest.' They must be worn for the battle with the sourhogs, and you can either get them with the quest or from any Slayer Master after the quest. You will need to complete this quest, to either get a pair of free goggles or to unlock the ability to buy them from Slayer Masters.