The Stongest Eidolon is the thirty-third optional quest. It can be obtained by talking to Priscilla after completing the quest Spirit of Water and defeating Ultima Weapon - it is automatically obtained if the former is done after the latter. Talking to Priscilla again will make her summon Eden, a superboss which must be beaten to complete the quest. There is no direct EXP or Gold reward for completing the quest, but Eden may randomly drop the Zodiac Escutcheon. Also, Eden can now be summoned at the Tower of Summoning though it is not as strong as Priscilla's version.
When Eden is summoned, there is a time limit while fighting Eden, if the time runs out before Eden is defeat, it will disappear and you will have to summon again and fight him all over again.
If the player approaches Frakir after completing the quest, he will talk to them and give them 25000 Gold and 3 Crystal Shards as a present. Completing the quest also unlocks the team Strongest Eidolon in the Battle Arena's Dimension Cup.