It turns out the 100,000 damage can be across multiple enemies. The Eidolon ultimate abilities can easily do plenty of damage without staggering.
I inadvertently got this while completing Cie'th Stone #55. Vanille was my party leader and I was doing the Death spam strategy to kill the Neochu. After it died, I summoned Hecatoncheir to finish the Picochus. I immediately use Gaian Salvo and it did over 100,000 points of damage across the five Picochus.