You can find Exodus in Mosphoran Highwaste after making Moogle, from Salikawood, to repair the gate. After that, moogles will come to Mosphoran and take care of Shrines of The Wind.
While being in the camp you have to activate south and north-west device. It opens the way to other locations. Leave the camp with north-east exit. You can see chocobo in front of you. Give him Gyshal Greens and go to the arena on the south from you. Turn right then and run on leaves to the rocky path. Face along it, until you get to the place that only chocobo can enter. You will see a T-junction on the next area. Run forward and proceed to the next area. You will be asked if you want to dismount from the chocobo. You have to say "YES". You will find here third device which you have to activate: the east one. Now leave the area, get back to the T-junction and turn left. At the top you will see another bridge made of leaves. The Exodus waits for you in the next area.
The numbers show the order of activating the shrines.
About 120 000 HP
Resistant to Libra
During that battle you cannot use items, which means that you won't be able to use the Chronos Tear, if any of your characters gets hit by Stop. Luckily Exodus uses that attack when the battle comes to end. It is useful to have Power Armlet.
Before that fight, equip one of your offensive mages with Opal Ring - Exodus's status is reflect, and Magick will be very useful during that battle.
Exodus is not the one with variety of attacks, but it doesn't mean that you should underestimate him. Mainly, he attacks with the ordinary attack (it wounds him also) and flare. He uses Scathe at the end.
Before the end he will use paling and the only way to defeat him is to attack with magick