Hiccup constructed several pair of Death Song Amber Goggles at some point prior to the "Dire Straits" episode.
When traders do not show up at Berk for several weeks, the Dragon Riders fly to the Straits of Baldur to investigate. They discover a Submaripper is lurking in the water. Hiccup, Snotlout, and Astrid return to the Straits to hopefully drive off the territorial dragon out to the open see. Hiccup hands out the Death Song Amber Goggles to the others so that they would be able to see while underwater. Hiccup realizes that the Submaripper is chained in place, and retreats to come up with another plan.
Hiccup wears the Death Song Amber Goggles again when he and Fishlegs experiment with different quantitative combinations of Gronckle Iron and Death Song amber to create an effective stabilizer that can prevent the volcano from destroying Dragon's Edge.
The Death Song Amber Goggles are constructed of a single thin pane of Death Song amber, placed in a metal frame. It has leather straps to affix around the head. The frame covers both eyes and the nose.
The thin amber allows the wearer to see out (albeit orange-tinted) into water, as the wearer does not need to worry about the water coming into contact with the eyes or getting up their nose.