Get 9 hamlet seals (3 inferno, 3 vortex, 3 tremor) hopefully from 60,000+ chests so you don't spend four years doing Hamlet and give them to Rowena while in possession "On the Properties of Beastmen" (which is 25,000 grand company seals) to get a Soiled Promissory Note which allows you to start the quest at Gerrolt at the Hawthorne Hut.
Apparently, since I obviously haven't gotten this far this is all conjecture/rumour/forum posts, the next step is to kill the Beastmen NM in their stronghold (for an "ancient/damaged" version of the relic) and then trade in a double melded class weapon. I said it above but:
Ahylogg Rah for Monk and Paladin
Lozol Totoloq for Bard and Dragoon
3rd Order Patriarch for Warrior, White Mage and Black Mage
The class-weapons and respective materia are as follows:
Mailbreaker with two Heaven's Eye IV for PLD
Avengers with two Manathirst IV for MNK
Obelisk with two Savage Might IV for DRG
Sarnga with two Heaven's Eye IV for BRD
Rampager with two Touch of Rage IV for WAR
Astrolabe with two Hell's Fist IV for BLM
Alkalurops with two Mind IV for WHM
Then you are sent to collect 3 Miser's Mythril in Aurum Vale. A sixth chest will now spawn in Aurum Vale when you complete it (afaik it always pops?) and the items go directly to you when you open (a la primal weapons). The drop rate of Miser's Mythril seems to be incredibly low unless you speed run (and 5 chest?) under 17 minutes in which case the drop rate raises astronomically (100%?).
Then you do the same in Cutter's Cry except for 3 Alumina Salt, and this must be done after the Aurum Vale step(?). Again 17 minutes seems to ensure drop.
You are now sent to collect a piece of literature on the Relic, I don't know if you just go to Gerrolt with this shit or not, but I assume so. In order to get the Relic books you need the following:
Enchiridion, which seems to drop from Dzemael Darkhold in a sixth chest a la the above step. Current conjecture I've read says under 15 minute (5 chest etc) ensures a drop, but that's a crazy moonspeak site.
Oschon's Finger, which comes from high-level Caravans in as of yet unknown manner to me.
Allagan Band, which drops from the boss of any Behest at the Lv40 camps that don't host Company Leves. For the stupid, that's Nine Ivies, Broken Water, and Iron Lake. You can obtain this item before you get to this step, unlike the above four items.
Beastmen Currency, which again you can get beforehand, in an amount of your choosing. The type of currency seems to correspond to the NM you killed for the broken weapon above. In the screenshot posted earlier, for example, they were doing Gae Bolg so they needed 990 willowknots, 495 mapleknots, or 99 ebonknots.
After this step I am even less sure, but it seems you obtain the "Unfinished (insert Relic name here)" items now.
Prevailing theories following this step:
Raise spiritbond on the Unfinished Weapon to max. (Note that the Unfinished Weapons "inhibit spiritbond," so I imagine this is rather annoying grind.)
Apparently some sort of Faction Leve exists which can now be flagged after the above spiritbond step which requires you to defeat an NM while equipped with the Unfinished Weapon.
Then you must clear Garuda and Ifrit (Extreme) while equipped with the Unfinished Weapon.
As the rumors go, the Primal fights are the final step and you are then bestowed with God's glory in the forum of a Relic Weapon you sick no-life bastard who's conned so many people out of Dynamis Currency after four years of hard work.