Both of you spamming fire arrows would mean that you're not doing much more DPS than if you just used wooden arrows, since fire damage doesn't stack. You'd be wasting more than 50% of the fire damage, so more than 1/3rd of your total damage is just not applied.
Wooden arrow does 22 pierce, while fire arrow does 11 pierce and 22 fire(DOT). I think elder does take increased damage from fire, so you're still better off with fire arrows, but one of you carrying wooden arrows instead would definitely increase DPS.

I recommend starting boss fights with 200+ effective arrows per player (although you probably already learned this). Also setting up a portal or a small base nearby in case you need to repair or craft something. One of you can just kite the boss, while the other takes a break.