It's funny how we describe Dark Eldar, arguably one of the flimsiest armies in 40K, as the rock to our scissors. I'd say they're more the scissors to our paper, as it goes. It's true that Dark Eldar are a tricky match for Tyranids, the ability to spam poison and darklight weapons renders our MCs incredibly vulnerable, and they can probably reliably outfight most of the rest of our units.
2 Flying Hive Tyrants with Hive commander and two sets of twin linked brain leach worms.
2 Squads of 3 Zoanthropes each
The Doom of Malentai in a Spore
1 squad of Gargoyles
2 Trygons with poison
2 Tervigons and 2 squads of minimal termagaunts.
The idea against the DE list was if I went first to fly the hive tyrants high trying to take out transports in the first two rounds of shooting and hoping that enemy flyers would not kill them both when they came in. If I went second, I would bring my hive tyrants in on turn 2 with a view to taking out his fliers first, then move onto transports subsequently. In either case I bring the trygons, the doom and the gargoyles in on turn 2 which should be more reliable with hive commander in play. That presents a very target rich environment for the DE on turn 2 (or 3) and should allow something nasty to get into him at that point.
It is likely I am going to have to play hide and seek with the Tervigons, Termagaunts and Zoanthropes in the first two turns which is why I choose the second squad of Zoanthropes over Hive Guard, even though the Guards are much better at shooting the transports. I think I need the Synapse cover and if I can get rid of the runes of warding, Zoanthropes can be very useful.
I have played this list against other opponents and find it to be very resilient, I am still to find my DE nemesis to play against again though, which was the inspiration for the list.
Does this give our scissors diamond tipped blades against the rock that was described, and where would it be weak against other forces.
It's hard to know in detail whether this list would be effective without knowing exactly what your opponent's army consists of, but as most Dark Eldar armies are Raider and Venom spam with flyers and Ravagers to fill, it's not too hard to guess.
I think, honestly, that you'd be better off swapping one of the zoanthrope units for hive guard, if not both. As Hive Guard can (I think) bypass their cover saves and are impossible to block LOS to, and as Dark Eldar vehicles without those defenses die in a stiff breeze, I think the zoanthropes are simply going to either blow themselves up thanks to Runes of Warding or do nothing while you try to kill off runes of warding. Hive Guard don't have to worry about that issue, and are therefore in my opinion a better choice.
That aside, I think that this would probably be pretty effective. I think you'd probably benefit from running the Trygons naked, as the re-roll to wound shouldn't really be necessary all that often. With that and the points saved from changing thropes to hive guard you could even bump one to a Prime and keep your synapse web in good condition.
Other than that, as long as the Tervigons have AG and TS I think you've got a good candidate here. A pair of dakkatyrants is a solid anti-tank force against Dark Eldar (especially when employing Vector Strike as well), and once the Farseer's in the open, kill it with fire