Step 1: Complete Main Scenario Quest, All Class and Job quests for that respective weapon.
Step 2: Talk to ‘Nedrick Ironheart‘ in Vesper Bay who will give you the quest ‘A Relic Reborn‘
Step 3: Talk to ‘Rowena’ in Revenant’s Toll
Step 4: Talk to ‘Gerolt‘ in Hyrstmill (Northwest of Fallgourd Float – take a Chocobo Porter)
Step 5: Gerolt will ask you to find your respective ‘Broken Weapon‘
Step 6: Present Gerolt with your Job specific weapon double melded with Grade III Materia. (either buy these weapons from the Marketplace or look below to find out how to get these weapons)
Step 7: Obtain ‘Alumina Salts‘ from fighting the D’horme Chimera in Coerthas (Northeast of Camp Dragonhead). You must defeat the Chimera as the Job you will get the relic weapon with. Once defeated bring the salts back to Gerolt.