Dual Halcyons are currently an extremely strong military strategy. The main weakness with it though, it that the costs of the two Halcyons can be very risky. Overall, targetting ther economy, not the military, is the way to defeat them.

TEC does very well against dual Halcyons. In this case, you want either an Akkan and Sova, or dual Sovas. The Akkan will obviously boost expansion. With the Sovas, you want to get ranks in Heavy SC and Embargo. Don't go for Bombers- get Fighter SC. Sova Fighters can adeptly handle Advent Bombers or keep their Fighters occupied. If you can, send your Sovas to your enemy's HW and Embargo him.

Vasari has a few less options. Dual Skirantras is can do well with Repair Cloud and Scramble Bombers, but early flak might be needed to handle the enemy Fighters.

Otherwise, make sure your fleet has many LRFs and Flak, the former for killing the Halcyons themselves, and the latter for supressing Fighters. Try to keep the enemy occupied while expanding and taking over their planets- the initial cost of the two caps makes their economy easy to damage.

EDIT: And in a team game, you really have to get feed.

Well, not guaranteed, but it is very likely.  Of course, don't underestimate the classics like the Progenitor.  I won a battle the other day with dual-Progen alternating shield restore.  Yeah, I also had a Halcyon, but I think we all know that the carrier caps are just standard fare these days.

First things first:  without feed, it's very difficult for an Advent player to hit hard with two caps at the very start of the game.  If you see dual Halcyon in the first five minutes, your opponent is being fed, and you need to ask your teammates for feed or fall back on the defensive.  Otherwise, you do have some leeway before he hits hard.

Now, the question is whether you lead with carrier cap or with colony cap.  The Halcyon rush has made me abandon Marza and Kortul starts; they're just too vulnerable to it if it's well played.  If you have a colony cap, you need to play your advantage.  The Advent player needs to drag around colony frigates everywhere he goes.  This will slow down his expansion and prevent him from grabbing important planets that may lie between the two of you.  You need to expand more aggressively in that early part of the game.  Even if you do get pushed back, that's an invaluable buffer and your ability to quickly get repair bays operational is a must.  If you have a carrier cap, you can set it to all fighter and this will keep the bombers thinned.  TK push and ADA together will prevent you from claiming air supremacy if he has two Halcyons, but anything you can do to reduce his bomber presence is critical.

In the actual fight, You want to push the confrontation into the mid-game.  The longer it draws on, the less of an edge the double-Halcyon rush has.  Even if you're losing a battle of attrition, successfully drawing it on to late game will even the scores.  With that in mind, your goal isn't to win, persay, but rather to force him to retreat.  To do this, you need to know what's coming.  You need to know whether those Halcyons are bomber-equipped or fighter equipped.  You also need to know if he's leaning more heavily on seekers or disciples.  If you see illuminators or even flaks as part of a dual-Halcyon rush, you need to ask for feed, because your opponent is getting lots. 

If your opponent has relatively few scouts and fighters, you should focus on spamming LRF.  These can cut down either on disciple numbers or directly focus on the Halcyon and force it to retreat.  Without scout or fighter presence, he'll have a hard time thinning out your LRF numbers effectively.  If he's a little shabby on his disciple count, you can bring out flaks, and these help enormously against strike craft and scouts.  Against a well-balanced Advent, you may need to bring in cobalts to help kill the scouts. 

Long-term, your goal is to raise up a good capital ship and have it lead LRF and flak.  A good capital ship killer like an Akkan with ion bolt or Jerrasul with nanos can force the Halcyon to just get the hell out of there.  On the other hand, Sova can be very helpful in clearing out fleets due to its strong combat abilities and the Skirantra is good for keeping your own units alive with repair cloud.  This also includes fighters; telekinetich push rarely kills, but often leaves them damaged, and repair cloud is one of your best counter-measures.

My last remarks are simply that this is a powerful strategy and there's no question that you're going to have to work hard to beat it (particularly if you're Vasari).  I easily slaughtered a Vasari opponent the other day as a dual-Halcyon Advent.  The replay showed why: I got feed and he did not.  As a result, he struggled to get a starbase operational but I was in the gravity well and hitting it with bombers before it was upgraded.  If he'd had feed, he would have had repair bays and hangers up in time to stop me from doing this.  The real lesson is to beware of the fed Advent player.

Mainly because I will kite my dual Halcyon's around the gravity well while my minimum of 8 bombers go after your Eggs. Plus I will probably have atleast 10 disciples following your eggs beating at it's shields and hull. If you go Assailant, I bring scouts. If you go Skirmishers I bring even more disciples or Illums. If you go Carriers I bring even way more disciples in. Eventually you will most likely lose or abandon your home planet.

Can't dual Sova do the same thing, only better?

maybe someone should start a 1v1v1 game of fairly skilled players, and have one person play tec, one advent, and one vasari, and have em set up an early game rush situation.

like, only research the upgrades you are likely to have early game or whatever.

but anyways, just get each of the races to face off in a 2 carrier battle, supported by a early-game replica fleet.

do a advent-vasari battle, advent-tec battle, and tec-vasari battle.

I know you said no theory craft, but oh well...  I'm not presenting this as fact.  This is sheer theory, but I'm thinking this would work...

For the Vasari (because I hate playing as TEC): Skirantra+Kortul.

Skirantra: This ship should be held back and should have its SC set to all fighters and be guarding it and the Kortul.  Ignore SB and go straight for Repair Cloud.  For your secondary, get MPA.  Your fighters need all the survivability they can get.  The point of this ship is to kill off their bombers that they send at you and if nothing else neutralize fighters.

Kortul: This ship should be up close and personal with the enemy ships.  You need DS to knock down their AM levels so that you can stop telekinetic push.  But the primary ability should be Jam Weapons.  You need to neutralize their fighters and bombers as much as you can.  Neutralize their SC presence and their main advantage goes away.

At the beginning of the battle, send your Assailants and Kortul to the front lines to blast away at any Disciples and have the Kortul target the Halcyons directly to wipe out their AM.  The Skirantra should be in the rear and hopefully aided by a repair platform or two (and maybe some missile platforms as well)  You want to be on the defensive when you do fight this battle.  You need that advantage.

As the fight drags on, keep your capital ships alive at all costs.  You need those abilities up.  If they go down, you die.  Plain and simple.  Also, any hangars you can get up to boost your SC numbers are going to be huge helps against ADA.  Eventually, you will drain his AM.  This will result in no more TP slaughtering your SC.  Without this, your Skirantra with its RC and MPA ought to give you an advantage, even if only slight.  This gives you the opportunity you need to kill his SC.

Once he has no more SC, you have the advantage as those Halos are sitting ducks for your Assailant army.  Yes, he will bring scouts, but your fighters (now that they have killed his SC) will have new targets.  Once he retreats, repair your forces immediately..

Also, if he brings out counters to your LRF's, get more hangars and repair platforms up.  Also, missile platforms are equivalent to about two Assailants, and scouts don't counter them.  So keep that in mind as well.  Also, get phasic trap up as soon as you can.  Between that and Jam weapons, his SC should be sitting ducks for your flak and fighters.

If he brings in Illuminators, get feed.  He is being fed, so you need that extra boost.  Get an Orky if possible, but make sure that it is within range of RC and your platforms when you do.  Once the Orky is upgraded, your victory is almost assured.  Highly upgraded Orkies are things of might.  They can also tank enourmous damage and since Halos don't really deal that much themselves and a single volley of PM's from an Orky deals 325 damage (let alone what happens if multiple banks fire at the target which results in more as the 325 is per bank, and it launches PM's from all four banks).

In other words, if he brings counters, you bring counters.  If he get's fed, you need to be fed.

Once again, this is only a theory, but I figured I'd post it so that if someone wanted to they could test it out.  I personally don't know, but it is logical, so a test to see how close it is and whether it needs some adaptations, should be abandoned, or does work.

TEC definitely has it easy with the Sova.  It counters both light frigates and scouts, and can negate a bomber-laden Halcyon.  However, you do have to be mindful, two Halcyons get four squads.  If he goes 4 fighter 4 bomber he can suppress your strike craft and then proceed to bomb your cap (key is to keep the bombers docked until he thins out your fighters a bit).  The difficulty is if you're Vasari or you didn't start with Sova.  Then you're in a bit of trouble.

This might be the only circumstance where having dual Kols may be remotely viable. Two Kols with Flak Burst cause just enough damage to kill all the Halcyons' Fighters at level 1- and their Bombers by level 3. Of course, a Kol and Sova combination would be far more worthwhile, since Flak Burst will at least damage their SC enough to let the Sova's Fighters have an easier time suppressing their numbers. Of course, this is all theory, and having a Kol in its current state past this point is virtually worthless.

Seriosly, with the same budget from the making of a second cap, you could park a entire squad of Cobalts/LRF/Garda  behind the Halycons and hurt them badly along with your Sova/Kol/Akkan since the Halycons can not fire their main weapons from their rear.  Any damage from bombers to your cap will be healed with a Repair bay.

only build one carrier cap*

Okay, I tested 1 dunov against 1 halcyon.  I played tec, I let the AI play advent.  Dunov got first level of magnetize.  Halcyon got first level of adept drone anime.

TEST 1.  Donov configured with 1 fighter, halcyon all bombers.  I tried letting the figher wing fly around, then I tried keeping the fighter wing stationary near an optimum point where the bombers were making passes.  The stationary approached seemed to be working better, so I kept it that way.  Dunov had to be micro'd to be right on top of the halcyon so that the bombers were forced to get in close to his own ship, allowing magnetize to have a chance at working (you have to magnetize HIS ship).

RESULT: Halcyon wins.

TEST 2. Dunov configured with 1 bomber, stationary and parked next to the halcyon.  Everything else the same.

RESULT: Surprise - donov wins.

RETROSPECT:

I realized after the tests on this pointblank map that the halcyon never had a chance to fully build up its initial bomber wings.  They initially spawned at 20% or whatever, and got to make a pass or two before I killed them.  If he had 100% of his strikecraft, my guess is the result could be different for test 2.

Also, I did not get around to testing 2 halcyons against 2 dunovs, as I wanted.  Plus, the sheer number of configurations possible makes this test almost impossible to do.  With this particular game, there is no such thing as playing by intuition, and there are no true counters to anything.  Any little small difference from 1 situation to the next will totally affect the outcome, and must be tested.

For instance, in the above tests, just switching from fighters to bombers, keeping halcyon constant at all bombers, there was a difference in outcome.  So how am I supposed to do this test for real?  How many combinations of fighter/bomber are possible between 2 halyons and 2 dunovs?  Also, what about levels?  All level 1?  Mixture of level 1 and 2?  If mixture, how should dunovs manage both magnetize and shield restore?  Etc.  Any of these factors could affect the outcome.

I cannot do this test completely.  But my intuition (which is good for jack crap in this game) tells me that in a real world situation, the "skilled" dual halcyon player will beat dual dunovs because 1) he isn't gonna sit still and let my dunovs get on top of him so that his bombers must get in range of his own ships, and 2) the sheer number of bombers from 2 halcyons can do a lot of damange in a couple passes before you can get off a good magnetize, IF he sits still and lets you get off a good magnetize.

Like I said, you can't intuitively figure out what will happen in this game like with other games.  You just have to test it "in the field" as we say in engineering lingo.  Thing is, the "combinatorial explosion" makes that somewhat impossible.

Question:  How much time and energy do you think halcyon spammers are burning up trying to figure out how to make their strat work?  Do you think it compares to the time and energy people are spending on the other side trying to defeat their strat?  There is an imbalance here.

At any rate, that's my attempt at a contribution to an answer, which wasn't very good, but at least I get an A for effort.  I'll wait for more real world answers.

I was thinking along the lines of Sova with Embargo.  But you certainly have Missile Batteries in your pocket, in case your recon finds out he's spamming Disciples.  Just leave the ability point unallocated until it's time to use it.  Sucks for him, not knowing what you're going to do.  If he chooses to go head-to-head with his Halcyons, go fighters and play D while you Embargo his butt.  That renders his TK push not very useful.  If he instead attacks your homeworld with his Halcyons, you go to his--and you have Embargo.  That also negates TK push.  Every cast of Embargo is like taking a Disciple out of his hands and giving you a Cobalt; and that's at level 1.  At level 2 (level 3 Sova) it's like taking away 2 Disciples and adding 2 Cobalts.  That almost makes it worth just buying the level.  If he comes at you with early Disciples, put your point in Missile Batteries instead.  If he comes at you with Disciples but it's in reaction to your Embargo, it's too late:  Embargo slows his production, and you have Cobalts and LRM of your own.

Anyway, not going to try it myself.  I think I'm going to retire from playing Sins soon (real life calls).

Once again, I would like to comment on my previous idea.  I suggested using a Kortul and Skirantra.  I spent an hour and a half thinking about it.  The more I thought about it, the more it makes sense.  I drew an image and a giant combat triangle/wheel to show the way things work.

Ultimately, the result will be can you kill his scouts and stop Telekinetic Push.  If so, you win.  If not, you lose.  The key is to use Phasic Traps and Jam Weapons to neutralize his SC.  That neutralizes one of his counters to your fighters.  The other is TKP.   By using MPA and RC you can repair any damage incurred by it until you run out of AM.  During this entire time, you use DS on the Kortul to knock down their AM.  The result is that while you run out of AM, so do they.

Without TKP and scouts, your Assailants are free to kill his Disciples, and without Disciples attacking them, your Sentinels are free to attack his neutralized fighters.  Without fighters, you gain air superiority.  With air superiority, you gain the option to turn fighters into bombers.  With bombers, you can quickly kill his Halcyons.

I would like to request someone to test this theory.  This is theorycraft, but without designing new solutions, we are stuck without a solution should a Vasari one not have been found yet.  I believe this would work, but it needs to be tested.