Spoilers in video and text below for a method to win Bonds of Friendship.
https://www.youtube.com/watch?v=jvNzI4VEkAI
I swapped out Enemy Skill for Revive which I don't think I actually used on my winning run, but did bail me out on a couple of earlier runs.
You are squishy, but with Genji Gloves and Magic Focus'd Aerogas with Faith on you blow enemies up very quickly while sustaining yourself so the runs become fast. With a bit of practice rounds 1-8 will soon become largely busywork (except occasionally 4 can get lucky bursts on you), round 9 is fairly repeatable once you figure out the right tempo to adopt (Hold ATB for the wings, then one Aerora each to blow them up, then get your licks in). I think if you get good enough at fight 5 you could probably ditch the Ele-Fire & Ice for stat boosts or w/e - didn't feel like I needed it once I got slick at handling him.
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