I found that the easiest way to do this is to look for one of the roaming patrols of five soldiers in New Orleans. The guy you want to stick with the berserk dart is the one wearing the admiral-type feathered hat (not a tricorner hat) that uses a cavalry saber and a pistol. He can take a lot of punishment and he's fast with the saber, so he works better than sticking one of the heavies with the big axe because they are too slow and get their hits interrupted all the time.
It's best to use the "lady" persona for this and use the parasol gun for your darts, because she raises far less suspicion than the other personas. Now just find a patrol. The patrols are normally five soldiers, so find one that has a path that passes near another group of soldiers. When the two groups are close together, stick the admiral dude with a berserk dart then stand back and watch the chaos. The admiral guy can usually kill the normal soldiers in one hit. It only took like 10 seconds for the admiral to get five kills and he actually ended up with eight kills before the other soldiers finished him off.
The achievement will pop immediately upon the fifth kill.