This is indeed a hard fight, but it sounds like your group was having trouble because they didn't understand the fight mechanics fully.
After beating one of the 4 other Destiny's Edge characters (Faolain doesn't care about Mr. Sparkles, apparently), The Grand Duchess will appear and begin channeling a spell. If she manages to complete the spell, the character you killed will be returned to the fight at full health.
What your group needs to do to win, then, is kill one of the Destiny's Edge Phantasms, target Faolain when she appears, and do enough damage (about 1/4 of her health pool) to drive her off. If you're successfully, she will taunt Caithe and disappear, but the Destiny's Edge Phantasm you killed will stay dead. So the basic strategy is something like this:
- Kill one of the Elites
- Attack Faolain until she flees.
That said, you still should work with your group to coordinate targets to focus one of them down. ctrl+t is the default setting for "Call Target", which should help the 5 of you coordinate your abilities.
Of the five mobs, you should kill Mr. Sparkles ASAP. He doesn't have much health, and there's no good reason not to - that's one less mob beating on your party, so burn him down as fast as you can.
Of the members of Destiny's Edge, Eir Stegalkin should be your priority target, since she does crazy AoE damage (Where was that back when we were struggling through the Ascalonian Catacombs, huh?). I want to reiterate this: Eir cannot be left alone. I went through Twilight Arbor on my Mesmer, and the first thing I did was drop a Feedback dome on Eir. Her first volley rebounded in her face, taking out a full half of her health! If your profession has some way to negate projectiles, throw it at Eir!
After you kill Eir, focus on Faolin, and once you drive her off, Switch to Rytlock. Rytlock has a lot of damage as well as some knockbacks, which made our group switch to him next (remember to call targets!). After Rytlock (and another phase with Faolain), switch to Logan, and finally, Zojja (who seems pretty ineffective, all things considered).
Once you beat the last member of Destiny's Edge, Faolain will taunt Caithe once more, and then leave, and you will get dungeon completion credit.