Defeating Shinryu Celestia without the Eidolon will not be a very easy task, but there are few tips on how to defeat her
The Battle of Judecca
It will be tough to win this fight with the cadets during the first playthrough, as Shinryu Celestia is LV50 and can one-hit KO the player. It is best to stay away to make dodging easier.
- The Avoid magic should be used.
- When Shinryu Celestia is in the dark the player should pay attention to the red eyes to dodge the following attacks by staying on one side of the area, then rushing to the other side as soon as she attacks.
- It is best to keep Shinryu Celestia in front. With ranged attacks the player can hit Shinryu's Breaksight strike stunning it and dealing many Breaksight strikes in a row until it recovers. However, as it takes numerous such Breaksights to kill it, and the player is likely to die in one hit, the cadets are likely to perish one by one
Also, I haven't read anywhere stating you get a powerful weapon for those who deal the finishing blow to Shinryu Celestia, but you do receive a Venom Bow and Crystal Ball for completing an SO Requests
There is an SO to avoid damage for two minutes that earns a Crystal Ball. Another SO for slaying Shinryu with the active leader appears, and appeasing it yields a Venom Bow for Trey.
There are additional Special Bounties that you can complete that will reward you without using the Eidolon
Platinum Bangle - Complete The Battle of Judecca on Agito difficulty without summoning Bahamut ZERO
Mythril Bangle - Complete The Battle of Judecca on Finis difficulty without summoning Bahamut ZERO.
Lunar Armlet - Complete The Battle of Judecca without summoning Bahamut ZERO.