In order to avoid any misunderstandings. Trifecta achievements are granted for completing Trial/Dungeon on HM, in a limited amount of time without a single group's member death. 
The Concept itself isn't bad and the existence of said achievement is motivating to improve oneself. Although it often happens to be an extremely stressful and lengthy endeavour.

The biggest issue in the equation is obviously poor game's performance, crashes and bugs not allowing for a smooth raiding experience. There is only so much you can blame on the player's connection and hardware. More often than not, the game just doesn't work. Think we have experienced it all. Crashes in situations where one's connection was fine. Recent flavour of the month were sudden drops in game's performance for certain people even though everything was fine in other titles and speedtests. And those are just general "technical" problems. Those are the main reasons for raids being called off before established raid times. 
Every trial has its own set of bugs. Sometimes you need to adjust to the "feature", other times it's just unavoidable and you hope it won't happen in your perfect run. Yes, the concept of certain mechanics is great but often implemented poorly causing accidental deaths that shouldn't take place, forcing the group to reset. Things like taunted thrash add suddenly doing 180 to erase one of the DDs or synergy mechanic not working. On top of that, tanks have to deal with global features like Block Bug. Every new update brings new changes and what comes with it: new bugs. Balance changes often require re-adjustment and even whole re-progressions what is not doing us any favours either.

The toughest part of Trifecta is the No-Death part, which is not individual but group reward. It means that the other 11 people must perform flawlessly without random issue out of their control. But at the end of the day, we are just people and potential mistakes are not being forgiven by the game. Without room for error progressions often last months and half of them won't reach designated goals, especially the more demanding trials. GS or RG Trifecta progressions are often turning out to be failing HM objectives to begin with. What signals that content is very demanding, few can flawlessly perform therefore greatly diminishing accessibility for larger groups of players.
Getting 12 well performing people is often a logistical nightmare also considering frequent need for replacements. Rotation of people occurs due to changes in their real life, allowing for playing for a certain amount of time only and for so long. Spending +/- 5 months, a few days a week in one trial is far from our dream.

Stress factor is the other big thing. Raiding playerbase is mostly made of working class people. Struggling from day to day so we can chill a bit in the evenings in hope to relieve some stress. But what would you say for stressing out even more in a raiding environment? Because that's what often most of us feel after an hour of unsuccessful runs ruined by minor mistake or game's shenanigans. 
Now, imagine placing yourself in the shoes of a new player who is willing to become a veteran raider hoping to get all the Trifectas eventually. If you are good enough to become a member of a Score Pushing group, it shouldn't take that long. But in case of being even slightly limited by hardware, connection or dexterity you are having a really long journey lasting months per progression. Having 7 of such to catch up with the prospect of another on the horizon is really daunting. 

Achievements should be in reach of even an average player for whom trial trifectas are far from. Therefore I propose to remove Trifecta achievements, leaving just the Challenger (like the first iteration of dungeons CoS, RoM, FH, BF and trial MoL). Keeping the more popular title as the main reward. The most challenging part will still be the No-Death but without other requirements would allow for a more diverse approach in setups and tactics. Splitting progression into 2/3 for respective achievements. That's probably also the easiest and the least work consuming way of releasing those tensions. As an alternative you could also categorize those as individual achievements, making it more accessible. Although that could lead to an increase of toxicity among players. The other idea would be to allow for certain amount of deaths to be forgiven and still grant the Achievement. But is it a flawless run at this point? The perfect solution would be fixing the game but how likely is that?