Accessory Quests have now been introduced with the Saint Nicholas event. I gave ranks 3 and 4 a try today since Water is my main element.
General layout:
Stage 1: 3x trash mobs
Stage 2: Mid-boss with no rage meter
Stage 3: Final boss
For Water, you'll want to bring overdrive gauge extension (Black Propaganda). I encountered a high debuff resist rate, so Mordred is recommended. You'll need overdrive extension for the R4 final boss regardless of element. The R3 final boss's raging overdrive can be bypassed with a sufficiently powerful Full Burst.
The trash are dangerous, especially in Rank 4. For water, the top mob has an AoE ATK buff. Kill it first and don't let it get the move off. The bottom mob has a high-damage single-target attack. Try and mitigate it. The second mob has an AoE that shouldn't do too much damage with ATK down debuffs. If it gets buffed, you're in serious trouble.
The Water mid-boss's overdrive attacks 8x for low damage. It's not too dangerous, but you'll want overdrive extension on it.
The final boss has an extremely dangerous raging overdrive, but it can be completely mitigated by Awakened Gaia. In R3, a Full Burst should be sufficient to nearly empty the Rage gauge. In R4, you'll likely be eating some overdrives.
Since this is a multi-stage fight, make sure your debuffs are ready each time for the next stage. You'll have to go all-out on the R4 trash because their HP is very high, and it's prudent to do the same for R3.
I easily cleared R3 despite forgetting to bring Sniper Shot. R4 is stupidly hard, and I had to use 2 elixirs to clear it. The first wipe was caused by both affliction resistance down and Black Propaganda missing the top trash mob, allowing it to buff the second mob twice. The second wipe was caused by the final boss's raging overdrive and debuffs falling off. On my second attempt, I was able to clear without an elixir. Once again, debuffs falling off on the final boss almost wiped me.
Drops from the second R4 attempt:
For your first clear of R4, you'll be awarded an SSR accessory. If you can clear it, it's a nice prize. Beware that multiple wipes can wreak havoc on your debuffs and make the fights much harder.