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.

Because the catalyst is extremely misleading. You need to get kills with the Perfect Fifth's explosion's [i]burn effect[/i] to get credit. It's really stupid because the burn doesn't do any meaningful damage. Best I found was to find an area with a Phalanx, and several Legionaires. Shoot the Phalanx shield to build up the Perfect Fifth, then shoot one of the Legionaires once in the body. The burn should finish him off. Slow, but it works, and if done right you can keep using the Phalanx to charge Perfect Fifth shots without killing him.

Are you getting kills using the explosion, or the burning after-effect of the explosion? As only the burn after-effect progresses the catalyst.

I believe the kills have to be from the burn effect not the shot itself or the explosion it causes. Taken psions might be too squishy for this.