If he's massing Halcyon Carriers with TK push, in all honesty you're probably not going to get much done with bomber spam. It may be a better bet to devote carriers to fighters to keep the air clear and deal your damage in other ways.
In general, first thing you want to get done when fighting any advent fleet is force their Progen motherships to die or withdraw. That's the main thing outsustaining your damage output.
Also Dunovs are great Against the Advent. They will allow you to deal widespread AoE damage and drain much needed AM from the advent fleet. No AM=no strikecraft rebuilt by carrier frigates & no shield restore from progen mothership & no massive AoE damage from Eradica & no more TK push making your bombers useless. If you can manage to run the Eradica out fo AM, actually using LF & LRM frigates for damage instead of carriers becomes a lot more viable.
That said, tryign a direct confrontation with a mature advent fleet late game is probably a bad idea for TEC in general- that's simply not playing to your strengths. The TEC is all about early game pressure and late game forcing the enemy into a war of attrition that their superior economy can better afford. They aren't given to clean decisive late game victories where they take the enemy fleet head on unless their early game pressure managed to cripple their opponent early game.
Now I'm sure this sounds rather abstract, so what do I mean specifically?
For one, the Advent is all about synergy- they lose a lot more having to divide up their fleet then you do. Not to mention due to the amazing potency of Ogrov Torpedo Cruisers, even very small TEC fleets can pose lethal threat to enemy gravity wells. As TEC you should be attacking on multiple fronts, forcing the advent player to divide up their main fleet to defend. Once they have divided up their fleet, and lost a good deal of synergy it should be feasible to start making trades- and again trading casualties is in your favor since the TEC economy can better afford replacing losses.
That said, pay attention to enemy movements- If they send their entire fleet against one small assault detachment, retreat that small fleet, and continue your assault at other undefended locations.
Not to mention simultaneously sending several smaller attack fleets to different gravity wells with Ogrovs generally means you're going to destroy some structures somewhere before enemy reinforcements show up(Ogrovs kill buildings FAST)- which can result in damage to Advent infastructure their weaker economy can ill-afford.
One of your absolute best tools against the late game Advent Fleet is your Starbase self destruct upgrade. I can't stress this enough- it's basically War of attrition given form. It will allow you to wipe out whole fleets worth of frigates that are anywhere nearby if you can create a good opportunity & will clear the air of strikecraft.
When you are engaged in battles your main focus is inflicting painful losses, and the Cielo's Designate Target is an extremely useful tool for this task as it enhances focusfire drastically allowing you to make key capitalships very dead very fast.
As for Specific tips depending on subfaction:
TEC Rebels:
You Have the Ragnarov- even if your bombers are getting scattered by TK push, that alone should be enough to start sinking Advent Capitalships- Inflicting the Losses the Advent can't very well afford. As always Progen Motherships need to die first.
The TEC rebels also get all sorts of benefits from bombarding planets so stay on the offensive- as described above attack mutliple enemy wells simultaneously with the aim of splitting up the Advent fleet and causing Casualties somewhere.
Due to their extreme expansion rate, the TEC rebels also ahve a ton of potential for ending the game early or achieving an utterly overwhelming economic advantage by the late game
TEC Loyals:
The TEc loyals will have a tougher time then their Rebel Bretheren. That said, at high ranks the Ankylon's Disruption Matrix is a dealy natural combo with Marza Missile Barrage & other TEC AoE such as The Dunov's EMP blast for the Advent. The AoE silence interrupts their Guardian shield projection and Progen Mothership Shield Regen channels which are two of their strongest tools for mitigating AoE damage and prevents them from casting any interrupts of their own(for Marza).
With the exception of repair platforms, the Advent have absolutely no hull/shield restore over times or damage mitigation abilties which are not channels- So Disruption Matrix pretty much leaves the Advent Fleet briefly almost naked, denied all of their standard counters to AoE damage.
The Ankylon's Group shield is also extremely useful against the Eradica Titan- It can singlehandedly allow even Frail frigates to survive a Malice+Chastic Burst combo at least once. This makes using non-carrier frigates late game against the Advent Rebels easier for the TEC Loyals them most factions- Take advantage of this and using kodiak(if you can control the bomber situation) or Javelis LRM frigates if you can't.
Lastly, if the game runs long, Novalith cannons can certainyl help. They can be used to kill off populace that could be sacrificed to Wail of the Forsaken and generally contribute to the war of attrition you're trying to fight by hurting the Advent Economy & perhaps destroying a few small worlds, distracting the enemy with the need to recolonize.
Anyway, hope this post has been helpful, If you have any other questions I'd be happy to do my best to answer them.
