A few weeks ago I started on the horrendous grind for the new Anima weapon, that is available to each class in Final Fantasy 14 as of the most recent patch. Last night I finally received my weapon, albeit only in its first stage at ilevel 170.
So here's how the Soul Without Life quest goes. First of all, you need to be level 60 and probably finished unlocking all the Heavenward zones/dungeons via the story mode.
The quest line starts in Idyllshire from Rowena (coord 5, 5) and then will have you hopping around from Azys La and Revenants Toll until it finally reveals you have to grind FATE's until you aquire 18 crystals.
To be more precise, you need 3 Luminous Ice Crystals, 3 Luminous Earth Crystals and 3 Luminous Water Crystals to trade for the Umbral Nodule.
To get a chance of the cyrstal dropping from a FATE, you need to get the highest rank possible, so doing them on your own isn't advisable. Make a party with some friends or browse the party finder to join a group.
The good thing about the Anima weapon quest, is that once you've picked up the quest, you can do the FATE's as any other class and still get the crystals. So I used this as a good chance to level up one of my other jobs.
You can go into the areas that are too high for your current level as long as you are in a large party that will keep the aggro off your character.
Coerthas Western Highlands (luminous ice crystals) - Level 50
Dravanian Forelands (luminous earth crystals) - Level 52
Churning Mists (luminous lightning crystals) - Level 53
Sea of Clouds (luminous wind crystals) Level 56
Dravanian Hinterlands (luminous water crystals) Level 57
Azys Lla (luminous fire crystals) Level 59
Once you have 3 of each crystal from all the areas, make sure to switch back to the class you accepted the quest with, then return to Syndony in Revenants Toll to get the Nodules. Then head over to Azys Lla to trade them in. You will then finally recieve your Anima weapon!