There's a 9% chance per run (30% * 30%) of Ifrit resisting both of the same type of break through 2 breakers on Turn 1. If that happens with an ATK break and Ifrit decides to Vulcan Blast twice on his opening turn, there goes that run.
This is why I run a DPS-light, redundancy-heavy team. Obviously the option isn't available to everyone, but I have:
Ramza (with Dual Wield) - Weapon Break hits twice, so twice the checks. This is usually sufficient on its own. If this fails...
Firion (with Power Break on Ifrit, Dual Wield) - I don't get DEF breaks up on turn one so the lost damage from not using Fin Briar isn't that big of a deal, certainly not a bigger deal than getting pasted on the first round.
Friend unit (non-Olives all have Dual Wield and some Ifrits have Power Break)
Ling (with Daunting Step) - only one check. Haven't had to rely on this yet but the option is there.
Physical damage is what kills you until the second Radiant Plume (and arguably after). If you have 50% Fire Res or more on turn 1, then with Barfira up, the first Radiant Plume does a grand total of no damage, because the Fire Resist debuff is applied after the damage, not before. This is why Focus turn one isn't necessary either and you can Provoke or Barfira with Cecil instead, get Embolden up with Refia, whatever.
Slower than running double (well, triple with friend unit) DPS? Yep. But I've also never lost a run. Redundancy, redundancy, redundancy.