Enter Svartalfheim and obtain the blessing of Dvalin.
Go find <a href="/mobs/details.html?id=609">Nidhogg</a> at the world tree. Make sure you're flying, as there is a random slay room inside the tree. Kill him and get bark corpse.
Find and kill <a href="/mobs/details.html?id=124">Angrboda</a> (WNEE from "The Edge of the Ironwood") and get feather corpse. Find <a href="/mobs/details.html?id=24">Thjazi</a> (WNENUN from "The Edge of the Ironwood") and go up to Skaldi then ask skaldi ring. She'll babble about freedom, give feather skaldi. She'll give you Fehu, the luck rune. Go down, remove weapon, wear rune and kill Thjazi. This is an annoying fight - you don't want to kill the bastard and he hits hard. You may need to flee and heal. Wait for Thjazi to shapeshift into a bear, flee. Wearing the luck rune allows you to flee into a hidden room with Draupnir, so get ring pedestal.
Go back to the alfars, ask Grer Dvalin and he will open the door again., give shards dvalin. He'll ask for the bark of the world tree and a magical ring. How convenient that you already have those. Give them to him one at a time. He'll do a little hocus-pocus and give you <a href="/items/details.html?id=751">Tyrfing</a>. Leave Svartalfheim, go back to Prince Angantyr and give tyrfing prince.