I assume this also applies to the Collective Members Killed list.
The Old Town West threat that features a Collective member is the culprit, more than likely. Possibly the encounters in the missions 'Be Your Own Boss' or 'Idol Threat,' but it's usually the Old Town West threat.
With the threat, you have two events stacked on top of one another - the threat, which has one completion target, and the Collective member, who is another.
If you kill the Collective member before you reach the threat kill count target, the Challenge will update and one of two things will happen. Either a) notoriety will drop to zero, and all opponents from the threat will disappear. Or, b) the threat encounter will continue as if nothing happened. If the former, then simply leaving the area and returning will allow you to complete the encounter.
However, if you reach the threat kill count target before killing the Collective member dies, notoriety will reset *and* the Collective member will disappear. And since the Collective member only spawns when the threat is active on the map, he'll never come back, for you to fight.
Idol Hands and Be Your Own Boss have similar outcomes, but with a different trigger. In both fights, the Collective member's scripting actually allows them to flee the fight, on occasion. This can happen if they hit you with the AoE disorientate attack, and although the mission will go on as normal if they do escape, you won't get progression for the challenge. Since you're effectively blind after being hit by the AoE, there's little you can do to stop them from leaving, other than to spam damage in their vague direction.
To avoid this happening, simply engage the Collective member from range, as their AoE ability is scripted on a proximity trigger. The Satchel Charge is the most effective option here, since you're low level during these encounters, and the Satchel's damage is disproportionate to its rank.
Now, in your current situation, it is possible to complete the Challenge by popping into co-op, and redoing these encounters, (start with Old Town West, as it's almost always this one that the client player is missing.)
However, since going into co-op can stop all of your challenges from progressing on the save file that you make when you leave co-op, (along with numerous other issues, such as causing map icons to disappear/reappear, removing drug pallets from the map, etc,) it's not advised that you keep the progress you make.
Simply go into co-op to get Chaos Tamer finished, and then hope/pray that Volition are capable of disentangling their spaghetti code and fixing this ridiculous mess.