I've beaten frost dragon. First of all, for the really hard battles, don't build or change your team for status effects. You only get to reliably land a status effect once per battle. The second application the bosses have like 90% resistance, and I don't even think it's possible to apply a status a third time. Frost dragon will be a 15-20 round fight, so bringing a shitty unit like Cyan just to land 3 turns of paralyze is a huge handicap. Another thing in my experience is don't rely on magic nukers for dps on the super long fights. Exdeath will get off about 8 rounds of Firaga at 20 mp per cast, then he's out of mana and dead weight. Instead, craft a copy of Cura and put it on Exdeath, make him another healer, let your melee do the killing. Another issue is that Fran caps at 4* which means if she gets focused, she's probably going to die. If you can field a full team of 5* units, use them.
When I killed him, it was with 3 healers spending most rounds casting Cura, Rain doing terrible damage mostly keeping up power break, and Lasswell taking out ~85% of the bosses health using Raging Fist (from Ifrit) over the course of the battle. Make sure to give the black choker (confuse immunity) to your highest dps physical hitter. Technically you could keep up BarBlizzara, but he only really does AoE cold nukes once every few rounds, and it's more mana efficient to just use another cura to top everyone off after the nuke instead of wasting mana recasting the buff constantly. When your units get confused, you can attack them to break it, or just ignore it and let the dragon break it for you eventually, which is what I did.
I recorded my kill, which you can see
here. In short, Frost Dragon is a big endurance test. If you can outheal his damage every round, there's not much going on mechanically. Preserve mana, top up with multiple units casting Cura, and whittle him down.