Instructions
Travel to Anvil, which is the large city to the far west on your world map. If you've been to Anvil, you can fast-travel there via the world map. If you've been to the Anvil Lighthouse, fast-travel here instead -- it's closer to the Fin Gleam Helmet.
Go to the western coast outside of Anvil, and swim out to the island. Kill the creatures on the island; then stand by the rock at the northern tip of the island. Face west and walk down into the water.
Cast a water-breathing spell if you have one. Otherwise, try to move as quickly as you can while underwater, so that you don't drown. Proceed westward until you get to a large rock.
Walk around to the right side of the rock until you find a skeleton with a strange glass helmet. Examine the body to get the Fin Gleam Helmet. Equip it to breathe underwater.