A bit more information on the enemy fleet would be useful(what was with the coronata?  And what does your fleet composition look like(whichc apitalships do you choose and what frigates accompany your fleet?)

Honestly the Coronata does have a -damage aura, but beyond that it's no more resilient then any other titan(the titans with repair/shield restore abilities are generally harder to kill).

If you're having problems killing it, it's likely either because of the Advent Loyal's supporting fleet or because you lack a strong supporting fleet(lots of carrier frigates mainly).

That said here are a few general tips on making the very resilient Advent Battleball die:

1).  First priority target is their Progenitor Motherships.  If the Coronata is outhealing your damage they are likely the reason.  progen motherships have the Advent's only "healing" ability.  Destroy them or force them to retreat and the only regeneration the Coronata will enjoy is it's base regen(unless it's defending in which case there could be repair platforms)

2).  Bring Dunovs.  Dunovs are incredible in general(Likely the best overall TEC capitalship these days, though Akkans are a better choice for your first capitalship), but Dunovs are especially potent against the Advent who rely on their shields and have always been rather AM-hungry(EMP messes them up hard)

3).  Lots of Carrier frigates carrying bombers.  Strikecraft and starbases are the only TEC weapons systems not reduced by the Coronata's -dmg aura.  Carrier frigates are by far the best late game frigate anyway, and the fact that their weapons bypass that aura makes them an even better choice against the Coronata

4).  Keep your frigates away from the Coronata or they won't be yours for long.  That's the other beauty of Carrier frigates- they can spend the entire battle fleeing and staying out of range of the Coronata's weapons while their strikecraft pound on it.  If the Coronata ever does get close, make use of their supperior manueverability to create some distance(fly in the direction the Coronata's back is faced so that it has to turn about to chase, by which point your carriers will have a sizable lead.

5).  This late in the game you should have a few Cielos with Designate Target.  It's an amazing focusfire tool for the late game, and frankly even if they get stolen it doesn't matter much because Designate Target requires research(so the Cielo will lose that ability when stolen by the Advent Loyals leaving it only with it's shitty basic ability).

6).  I would just like to reiterate that most of the Coronata's staying power usually comes from the fleet around it.  Progen motherships restore it's shields, Rapture Battlecruisers debuff your frigates, and Iconus Guardians redirect a portion of the damage dealt to the titan to themselves.  Remove these allies or deny them AM and the coronata gets a whole lot softer

All that said though, in general it's not really advisable for a late game TEC fleet to attempt direct confrontations with the Advent Fleet.  The Advent in general is all about using synergy between ships to create an obscenely strong late game fleet.  In a direct confrontation the TEC, who's focus is on a strong economy is at a pretty big disadvantage.

The TEC are all about forcing the enemy into a war of attrition which they will win as the TEC's superior economy results in them having an easier time replacing destroyed ships then other factions.  As such they are less about clean decisive victories then the other races- they focus on creating messy situations where both sides will end up taking casualties.

One major tactic for use against Advent as TEC is to attack on multiple fronts.  Due to all the synergies an Advent fleet is stronger then the sum of it's parts- Conversely this means that the Advent lose a lot more from dividing their fleet up then the TEC fleet does.  Attack them on several fronts and force them to divide up their fleet- once they do it'll be much easier to cause casualties.  If they send a large portion of their fleet to one of your attack targets, retreat from that well, but keep up the assault on any wells that have yet to receive reinforcements.

One of the TEC's greatest tools for this kind of warfare is the Ogrov Torpedo Cruiser.  This Nasty ship allows even very small TEC fleets to be a mortal threat to even heavily fortified worlds.  They shred orbital structures, and if you're attacking on multiple fronts, the enemy will often slip up somewhere...and with Ogrovs even a slight slip up usually means losing several buildings.  As discussed earlier, replacing siad buildings will likely put more strain on other faction's economies then whatever you lose in failed attacks(especially if you choose high value targets such as Trade Posts).

The TEC rebel's bonuses to offensive play(bonuses related to planetary bombardment) promote this style of play even more by encouraging you to stay on the offensive.  Early game the Corsev can also be a great choice as it's Demolition team is perfect for causing a ton of enemy casualties.

Well to be fair, most of that isn't really as relevant as you are playing against hard computers(hard & high comps cheat on resources so you are less likely to overpower them through attrition).  That said, regardless of faction, decisive direct confrontations are entirely possible to win when fighting computers regardless of faction(The computers are kind of stupid when it comes to commanding battles).  To really give more relevant advice against computers I'd need to know a bit more about your fleet composition  and that of the Advent Loyal computer.

Well I suppose not every faction gets a weapon that on average increases damage by 66-99%(depending on enemy shield mitigation).  Most factions have to settle for max weapon upgrades of 30%.

 (Yes I'm one of those guys who's still bitter about phase missiles after all these years)

I think you're mad because you lost to a Coronata and don't want to admit it. Maybe boshimi unity massed your cookies into pudding or something like that.

Domina Subjugator do have a hull heal.  but the heal is on a longer cooldown then duration, requires 6 hostility labs & 2 researchs to unlock, and most importantly the frigate that casts it has a mere 550 hull+300 shields.

With titan AoE, Subjugators are unlikely to live long enough to cast their heal more then once.  It's not so much long term sustain as a single buff heal over time at the start of the battle- at which point the Coronata may not have suffered any hull damage yet anyway.

They are just too frail to really be a sustaining factor once titans hit the field.  Also It's ot always wise to go 6 labs deep in military these days as Advent.

So honestly yes, the advent does have another heal, but it's rather impractical so I didn't really see fit to include it in my advice/considerations.

Its the high level armor and mitigation values coupled with suppression that start to cause a problem for fleets. Its vicious when the ai researches the armor upgrades at tier 6 and 7 (these 2 tecs almost double the armor points) and shield mitigation bonuses at the end of the shield branch. 

hehe

this was special 

Okay, this I've missed completely...what's the issue with phase missiles?

-Twi

Aren't advent ships cheaper though?  And use less fleet?  Yeah, theyir hull is weaker, but fleet for fleet doesn't the hp mesh up pretty close?

(I'm not sure about this, actually asking here.  I haven't compared ship stats since early entrenchment.)

-Twi

The early game ships are very slightly stronger(mostly Flak & Light frigates).  

That said, it doesn't come anywhere near making up for how vulnerable they are to phase missiles.

Besides, the real area phase missiles are a threat is to capitalships- And guess what? Advent Capitalships cost the same as everyone else's and start with about 1000 less hull(and gain 20-60 less hull per level).

Another issue is that fully teched phase missiles do more damage per second while shields are up then down.  Realisticaly speaking phase missiles will actually kill a capitalship with 2000 shields & 2000 hull FASTER then they will kill a ship with just 2000 hull & 100 shields.  The high shield values on advent ships actually make them die faster then they would with lower shield totals.

then again, Advent are just the race hit the hardest.  At the end of the day phase missile research ultimately increases damage 2-3x as much as pretty much every other weapon type in the game(fully teched 66-120% increase as opposed to most weapon type's +30% when fully teched).  The biggest problem is that the no contest strongest weapon type in the game happens to counter shields- which are sort of the Advent's main combat tool.

That's racial....