I'm a believer that you shouldn't NEED discord or other tools outside of COH to get these badges, so other leaders may have better success rates using those kind of tools. But, consider for a second what is required of a league leader going for Triple Threat. You're looking for a narrow window when:
Chimera has just teleported, and you've allowed enough time for anyone he teleported from the other teams to return to their assigned AV
Nega's shield is not up, which is not something indicated in the game only inferred by the rage bar status (or someone very good at reporting it)
There's still time left on the clock for this phase
All AVs are at 2% (or, gulp, 1%) so they are close enough to be taken down quickly
If you can hit that window perfectly, you still have a decent chance of failing because after you give the kill order any of the 3 AVs can regen. Some have speculated that these regens are predictable, but I haven't found them to be. I've used timers and never found a consistent length of time between regen ticks. It appears to be like other things in the game, where the percentage chance of it firing goes up with time.
Once you give the kill order and the first AV falls, you only have 5 seconds to put down the other 2. So, there's a fair bit of luck involved even if you do everything right.
And then, even if you managed to do all that, you have to make sure not to kill Tyrant too fast in the final battle or it could bug out and no badge.
I've said many times that Magisterium needs fixing and I hope we get an update for that soon.