"Intended" way? Be geared and skilled enough to kill everything even when it's buffed. No way you can track which of the dozens of targets on screen are newer or older to optimize your kill speed. Just keep firing.

Mines, mines, an more mines, maby add another mine, jus in case.

You don't need to clear the HRA. You just need to kill enough for the boss to appear. I never felt that modifier particularly difficult. I actually totally ignore it. That is, I don't adapt my play style in any way.

Vigilante Swift Executioner, on a Sentinel, with a Together We Stand Rakhima's Foresight does the trick.

20% reduced ramp up because of Sentinel passive and %50 reduced ramp up form Foresight turns the Executioner into a monster.

One shot one kill all the little stuff is not affected by the modifier.

I put an evolution catalyst on one and wound up with this

10% bypass shield
10% bypass armor
Killing an enemy temporarily increases the damage by 1%-25% for 8 seconds
Fully charged shots destabilizes the target for 8s.

I added the full Vigilante set and paired it with a Chaos Ragnarok and Thundercore.

With the right attributes and other gear you almost have to try to die.

If you purchased the Titans DLC, i would recommend the Parasite Mines. They deal damage over time, actively target new Prey and distract Enemies. Its like you have a whole Squadron of Drones fighting for you.