Holy Trinity can refer to two different Advent strategies.
The original strategy was to use a Progenitor Mothership with Malice, a Rapture Battlecruiser with Vengeance, and a Radiance Battleship with Animosity and Cleansing Brilliance combo. The strategy has fallen out of favor because of a capping nerf to Malice a long time ago.
This tactic works by having a Radiance use Animosity to force enemies to attack it, while a Rapture uses Vengeance to reflect the incoming damage back on the attackers. Malice allowed this damage to be multiplied across the entire enemy fleet, which could actually cause the enemy to take more damage than they received. Malice now has a target cap, so it is no longer capable of ravaging entire fleets. The combo still functions, but the number of capital ships required makes it highly impractical for what it does, and it can no longer be used stand-alone without a supporting fleet.
This combo is easily countered by applying any form of healing within your fleet, since the damage is diffused over a large number of targets. The presence of Hoshiko Robotics Cruisers, a Progenitor Mothership with Shield Regeneration, or a Skirantra Carrier with Repair Cloud drastically reduces the effectiveness of this combo. The ease with which this combo is countered by any faction, compared with the difficulty of fielding it, means that it is virtually never used in competitive play.
The modern version is to use a Progenitor Mothership with Shield Regeneration, a Rapture Battlecruiser with Vertigo, and a Halcyon Carrier with Amplify Energy Aura and Telekinetic Push. Such a fleet should always be supported by Iconus Guardians with Shield Projection and Repulsion.
This combo works by stacking multiple forms of damage reduction to reduce incoming damage to negligible amounts. This damage is then diffused by shield projection, and immediately healed by shield regeneration. Using Repulsion to cycle injured units and give them time to heal, this can make the Advent fleet effectively impervious to most forms of damage so long as they have antimatter. The Halcyon rounds out this combo by offering defense against bomber attacks and boosting damage output.
The Rapture Battlecruiser with Concentration Aura and Aeria Drone Hosts to provide additional strike craft is also a viable tactic with the strategy. Concentration Aura increases the damage of all of the carriers' strike craft, which gives such a fleet considerable firepower.
The best way to combat this strategy is to use the Vasari Phase Missile weapons. Since these bypass shields - including Advent's high shield mitigation and the shield projection of the Iconus Guardian - much of this defensive combo does not count. This is best combined with the Stilakus Subverter, which can disable Advent units entirely and further disrupt this combo. Advent players in this matchup are advised to eschew shield-based defense and focus all their effort on their damage output, relying on repulsion as their primary defensive tool.
The TEC faction has effectively only one option: the EMP Charge of the Dunov Battlecruiser. This removes antimatter and shields in an area of effect, which is useful against the tightly packed formation Advent players will need to employ to maximize the effectiveness of this tactic. However, a good Advent player will cycle units using repulsion to reduce this effect, so you'll still need to outnumber him significantly to have any chance of a decisive win. Your best approach as TEC is to strike early, and never give the Advent an opportunity to get this combo to maturity.