This achievement isn't as hard as some people make it out to be. Honestly, the real difficulty lies in making sure NPC cops don't steal your kills, and a degree of luck if somebody decides to go traitor.
The trick is to kill the people as fast as possible. Once the level is in progress, people are separated, and there's a chance that while you're finishing one robber off, another will make it to the getaway vehicle. Even in the beginning round, when nobody has any money to buy weapons with, you can easily kill somebody with the starting SMG. Just aim for the feet, so that when the person goes "Down Not Dead", no wasted bullets go in the air. If you fail to kill them with the first clip, don't reload, just switch to your pistol and pump them full of lead. It's faster, and you can reload afterward. Just repeat this process with each person, and you can get the majority of the group killed before they leave the loot area.
But what weapons are the best, if you don't draw the cop on the first round?
The first trick is: If you want this achievement, always buy weapons assuming that you'll be the cop. It might not outfit you perfectly for the actual level, but you weren't trying to get to the end anyway, were you?
The weapons you want are (depending on rank): The Kalingrad 74 (I believe you start out with it, correct me if I'm wrong). It's a good short-to-mid range weapon, and that's the range you'll be poppin' perps at. The Gras 12 (Unlocked at Rank 3, I believe) is probably the best shotgun in the game, because unlike most of the shotguns, it has an 8 shot clip, but a similar fire rate. However, the other shotguns can be used to effect. The Wasteland Hawk (Rank 3, again) is a brilliant pistol, and a three-shot spread to the chest will knock most people to the ground, to be finished easily. It's only $30,000, so if you came out of a round poorly, it can round off your setup nicely. Stay away from the snipers. At long range, human players still take three sniper shots to down, and another one or two (depending on placement) to kill. At that distance, you're bound to miss one shot, and the reload delay means you'll be outed quickly.
If I got any details wrong (such as shots to kill/down, or unlock ranks), please clarify in the comments. Also, if you've noticed any guns that work well, please tell me, so I can try them myself/add them.
EDIT: Also, a quick note: Remember that if you're the Undercover Cop, you ARE a cop. That means all NPC cops/goons are on your side and won't shoot you. And if you shoot them, it marks you as an undercover cop, and even if you manage to kill all of the other players, you still technically failed your mission, and can't get the achievement. (No, it doesn't make sense that the "goons" are on your side. But they are.) This makes the "Financial" map one of the harder maps to do this on, as the loot is carried by goons in the beginning, and you'll look suspicious not shooting at the start. However, I have completed the details of this achievement on every (non-DLC) map, so I feel that this guide is adequate.