Okay so I have been farming my Atmas and as you all know, it is pure torture. However, there is a guide for it and this guide has helped improve the torture to being mildly painful instead of "omg I want to murder this game" painful. So first, here is the link to the reddit site if u wanna go there and scan through it but I am just gonna copy paste what the guy said cause I am a lazy bastard. ENJOY!:http://www.reddit.com/r/ffxiv/comments/234sv4/atma_farming_theory_worked_for_me/
–––––––––––––––––––––––––––––––––––––––––––––––––––

I'm sure some of you have seen the Jp Atma farming theory and for me and my fellow FC members this method has worked based on our own personal server time. I've gotten the Atma from the zone within the hour (usually first 15 minutes of farming) so far 7 times in a row. If this is RNG it's pretty good lol Don't tell me you got it outside these times! Its very possible to get it outside of these times but a higher chance within these times.
Atma of the MAIDEN - Central Shroud - 1:00
Atma of the SCORPION - Southern Thanalan - 2:00
Atma of the WATER BEARER - Upper La Noscea - 3:00
Atma of the GOAT - East Shroud - 4:00
Atma of the BULL - Eastern Thanalan - 5:00
Atma of the RAM - Middle La Noscea - 6:00
Atma of the TWINS - Western Thanalan - 7:00
Atma of the LION - Outer La Noscea - 8:00
Atma of the FISH - Lower La Noscea - 9:00
Atma of the ARCHER - North Shroud - 10:00
Atma of the SCALES - Central Thanalan - 11:00
Atma of the CRAB - Western La Noscea - 12:00
You have to use your server time. People on the same server have different server times depending on where you're located, so look! Am or PM doesn't matter. Please post below if you've gotten different results. EDIT:All areas have the same drop rate, if you are in the area with the time and matching ST it's like an increased drop rate.
Edit: [–][Bah] [Lizi] on [Ragnarok] 5 Hours and no ATMA. Tryed this thing and got 1 in first FATE and another in 6th FATE.
Abra Hadabra worked for me as well.