This link might help you. http://ffxiv.consolegameswiki.com/wiki/Up_in_Arms... I'm not sure where you are in your quest, but if you have already completed the parts where Gerolt sent you to fight Chimera, then Amdapor Keep, then Hydra (Rowena sent you there, I think or maybe she sent you to the Keep), then the three hard mode primals, then you came back, you would give him some oil, then you take the weapon with 3 bottles of Thavnarian Mist to the furnace on the same platform as Gerolt. Make sure you have another weapon on you, because you have to "trade" the weapon and mist. Doesn't matter the level of the replacement weapon, because you're not going anywhere. Make the trade and the new Zenith weapon is now in your inventory. Equip that and then go talk to Jalzhan who is on the platform in the same area as Gerolt. As a matter of fact, as you stand at the furnace, turn left and he's across the grass. His quest DOES NOT sit on your quest list. It goes into completed side quests (he tells you this if you read all of his words). The first link I provided you will give you the list of areas you grind for Atma stones. Doesn't matter what fate, just make sure that your Zenith weapon is equipped while you take the fate. Don't worry about whether you get bronze, silver or gold. Don't worry about what time it is. There's no logic to the drop except pure RNG (random number generator), so just complete fates as time goes on.

Good luck.