There are four "worthy opponents." They are all located in Archylte Steppe, and they are all associated w/ missions for their respective Fragments:
1. Immortal - Spawns in the southeast section of the map when weather is cloudy. 2. Long Gui - Spawns in the east section of the map when weather is sunny. 3. Ochu - Spawns in the west section of the map when weather is rainy. 4. Yomi - Spawns in the southeast section of the map when weather is thundery.
The missions to defeat these four bosses are the final missions of the area and should become available after you are able to ride Yellow Chocobos (and also note that Yellow Chocobos are required for 100% Map Completion of Archylte Steppe). Use the weather manipulation machine in the chief's hut in order to spawn them.
(COM) Chichu: lvl 70 Str 1078/ HP 7841 / Infused - Resist Mag/Phy +36%, Role Resonance, Str: +35%, Auto Bravery, Jeopardize, Adrenaline. (SEN) Pulsework Gladiator: lvl 29/4671 hp
Start of battle Sab/Sab/Sen keep using poison until it sticks to Yomi, I suggest having Sarah lead for her Poisonga. Switch to your healing set if needed. Then go Rav/Rav/Sen using Thunder till staggered if he puts his shield before you can stagger him it cancels and sets back to 0. When his shield is up buff your party with everything you got. Shield goes off keep poisoning him when its removed on him. If
If you can manage to stagger him switch to Com/Com/Com and you will do massive amounts of damage cutting the battle time allot. Basically Poison till it sticks, then stagger him, his shield is up buff and heal. And he is done.