Save at the Save Station and continue. When the boss battle begins, restart it and try again - when the main menu comes up, equip both girls with Bangles, and make the following Paradigms.
Eidolon Battle: Hecatoncheir
Easy enough. Have Fang and Vanille spam debuffs for a steady rise in the Gestalt gauge. When it sprouts its tentacles, switch to setup to keep you healthy, then back to or until you can press Square/X to win the battle when the Gestalt gauge is full. Hecatoncheir will stand motionless for quite a while, and this is the best time to spam it with debuffs. It’ll attack a couple of times before returning to its motionless stance, and repeat the pattern.
You’ll obtain the Hecatoncheir Eidolith Key Item after the battle. Vanille’s ATB Gauge will increase by one segment, bringing her total to 4 (or 5, if you already bought the ATB node at the Crystarium).