As Yashnaheen said, you don't need Atonement, although it would speed things up a lot. /RDM is necessary. I kept stoneskin up because I didn't want to have to rely on my MP for curing and stoneskin is far easier on the mp than curing constantly, but your mileage may vary. The only thing that matters is you figure out a way to kill the avatar before the 30 minute mark.
It's on that count, too, that I list my least favorite of the avatars. Leviathan can be such a **** through Spring Water spam. You can recover from it, but it gets difficult when every time you get him to 20%, he jumps back up to 30% and you're getting close to the 5 minute mark. However, chances are, if you survive the two-hour, you'll be fine. Even if you don't, if you fight far enough away from his starting point (the bend works wonders), you can reraise and will most likely have time to kill him. Just don't fight at the top or near the top and try to cast spells within about 20-25 yalms of him - the avatars seem to have enhanced magic aggro detection.
Here's a link to the guide I used to start my avatar hunts: http://ffxi.allakhazam.com/db/jobs.html?fjob=5;mid=119022738016956122
Leviathan - PLD90, BLU90, MNK 90, DRG 78