Most of the crafting related achievements in The Lord of the Rings: Return to Moria seem to require you to craft all of the items on the same world with the same character. If you have any issues then re-crafting the items seems to fix it most of the time - otherwise switching between campaign & sandbox then trying again has also worked for me.
To unlock Westgate Weaponcraft you need to craft the following weapons:
* Iron Sword
* Iron War Axe
* Steel Sword
* Steel Battleaxe
* Last Alliance Maul
* First Age Sword
* First Age Greatsword
* Hunting Bow