Remember the Rat Tail I talked about? Now you can exchange it for an Adamantite. Well, you can't really use Adamantite as a weapon right now.

Take the Hovercraft to Mythril town, ride the Hovercraft to Adamant Isle Grotto. Then talk to the old man to exchange the Rat Tail for Adamantite.

Once you obtain the Adamantite, go into hollow Earth then head south to Kokkol's Forge. Talk to the old man upstairs and give him the Adamantite. That's it for now, we'll get back later after he finished forging a new weapon out of Adamantite for you.