Against Fire? I'd assume they'll have no issues, with Cthulhu and Water Raphael working on those Orbs.

Off element? Unknown. The good news is, HP Relic Joan with Water Raphael can drop damage by 90%. When combined with any Dragoon of the proper element (SR or SSR), you can mitigate 100% of damage... twice. That leaves you with... something like 18 turns to deal 7.5m off-element damage. Should be doable.

There's two problems though. This means that you need to have access to ALL element of Dragoons. SSRs can just be bought for a mere 10k Eidolon Orbs. One or two is doable. Six? ... that's a lot of work.
Secondly, you might get torn down by the normal attacks. If you don't get your atk debuffs to land, the boss will hurt a lot. Losing out on a full burst during those 18 turns might cause a wipe.