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.