It doesn't explain itself very well. If the Perfect Fifth shot kills the target on impact, it won't count. If the Perfect Fifth explosion kills the target, it won't count. Only if the target survives the hit, and the explosion, and dies due to the subsequent burn, does it count towards the catalyst. So you need an enemy that can survive the hits but be left with as little health as possible so a few ticks of damage kills them before it wears off. I quickly ground it out in the Castellum, on the Leviathan. I would get three precision hits on any target, then shoot an undamaged regular trooper in the head to activate perfect fifth. I would then body shot that same enemy with the perfect fifth shot. After the explosion, they were left with just a sliver of health which the burn would deplete, giving me a kill count on the catalyst.