I like eRe4s3r's 'lives' idea as one option, and I think it's a good one.
Another option would go along the same lines as eRe4s3r, except instead of having, say 3 tries, if you hit the wrong enemy, you get a countdown because of temporal instability. Within this countdown you have to kill a correct monster or you lose the mission. This helps with the situation where you accidentally killed the wrong monster because it was in the way.
Another idea is to have the wrong monsters fight the right monsters at the same time that they fight you. This could happen only around the player character as he moves around so that you won't get all of the monsters eliminating each other within 30 seconds of the mission, but the idea is that you can see that there are 2 sides (the monsters that belong and the ones that don't) and you have to 'choose' which side is the right one. This should be much easier than not having any idea which monsters don't belong. Plus, monsters fighting monsters is awesome. Oh, did I mention that the game should feature monsters fighting monsters since it's awesome?
I think an advanced version of this mission would be great (using eRe4s3r's last point): it would give you 3 tries + the ability to cancel a missed attempt if you hit the right monster within the countdown (ie. the combination of my idea and eRe4s3r's idea.) The trick is, you have NO IDEA what the criteria are. It could be anachronism, it could be by element, it could be by flying monsters vs walking, it could be technological monsters vs organic, you've no clue. The idea here is to use your deductive powers to figure out what the criteria are before you kill too many monsters and lose. This is where the mission type switches from memorization to deductive abilities, and IMO where it becomes amazing. Of course, many different possible criteria need to be programmed in here, but all of them must make sense. When you lose (or win), the game reveals what the criterion was so you're not left wondering and cussing.