This cannot be happening.Lightning
Odin inflicts Doom on the party leader at the beginning of the battle, and instead of being defeated, Lightning must fully fill Odin's Gestalt Bar. Odin is an aggressive Eidolon, initially targeting Hope with physical attacks and the occasional Thundara. Libra will reveal that Lightning can satisfy Odin by building chain bonuses and healing.
Lightning will need to do both as Odin's strikes will necessitate healing greater than Hope can supply. Odin will often guard with Ullr's Shield, allowing for a quick healing break or uninterrupted attacking phase.
A good strategy is to use Lightning as a Medic and keep Hope as a Ravager whenever Odin is in attacking mode, or when Hope is getting low on health. Whenever Odin takes a defensive stand, or when the health bar in both Lightning and Hope is full enough, the player should use both as Ravagers. Considering Odin will alternate between attacking the two for unspecified periods of time, another good strategy is having the one he is not attacking as Ravager and attack Odin continuously with magic, while the one he is attacking does the healing as a Medic, then switching the roles when he turns his focus onto the other character.
Since it is a test of Lightning's strength, the Gestalt Gauge fills faster when Lightning is the Medic than when Hope is. Therefore, the two best paradigms to use are Yin & Yang (MED/RAV) and Slash & Burn (COM/RAV). Odin is powerful, so it might be a good idea to have Hope start the battle as a Synergist so he can cast Protect.
The player can also start in Symbiosis (MED/SYN) for Hope to get Protect and Shell up. For attacking, the party should switch to Yin & Yang with Lightning as the Medic and Hope as the Ravager. When the party needs to heal, the player can switch to Double Dose (MED/MED). When Odin uses Ullr's Shield, the party should switch to Dualcasting (RAV/RAV) to drive the Gestalt Gauge up.