This solution is if you're not in a boosting group and want to do it on your own.
As mentioned previously, you have to do this on a Defiant map pack, most likely Condemned, and you have to be the last uninfected player at the end of a round. You will have three chances each match, so if you get infected early on, don't worry. Calm down and try again, and maybe put the controller down so you don't get frustrated and off your game.
Here are a couple strategies to help you if you're having trouble. Use whichever one you prefer, or switch between them if you're having a lot of difficulty.
1.) Safety in Numbers: Find a group of uninfected players who are camping one spot and team up with them. Try to stay as far to the back of the posse as you can, and simply dodge zombies as they mow down the players in front of you. Have your shotgun out, not your pistol--you want to kill people going right for you, not people far away who will take out the other survivors. Do NOT focus on kills or score, just staying alive while watching your allies bite the dust.
Pros - If you're not good with pistols or judging shotgun distances, other people will "help" you out, and the zombies aren't going for you.
Cons - If it gets crowded, it also gets hectic. If you lose track of a zombie, it's over for you that round.
2.) If You Want It Done Right: This is the opposite of the above, where you stay away from all the other players and obvious camp spots. You're going solo, but again, you're NOT focusing on kills. Hide, hide, hide until everyone else is dead. Around corners, above eye-level, wherever you can, and wherever groups of people aren't. Infected will go for big groups for a better chance of getting one before getting gunned down, but they'll also go right for you if they see you alone. If that happens, relocate to a different hiding spot so they'll give up when they can't find you.
Pros - The zombies will mostly ignore you, because they'll go for the obvious camping spots where they have more chances.
Cons - You'll have to be good with the pistol, the shotgun, or both. If one of them finds you, more might break off from the horde and overwhelm you.
And now for general tips on both strategies.
1.) Besides the Points: As I mentioned, ignore kills, score, and everything that isn't directly related to surviving the horde. Having the most kills doesn't always equal surviving the longest.
2.) Boom, Boom, Bash: If you're getting rushed, use your shotgun. If there are more than two coming for you, you're shotgun will only be fast enough to take out the first two. Don't even try to fire a third, you won't make it. Instead, after the second shot, immediately melee. It gives you a chance of blocking a sword rush.
3.) Every Man For Himself: Don't fire your gun unless you are in immediate danger. Let everyone else use their ammo, run low or run out, and get gank'd. Saviors aren't always survivors, and they're not your teammates. They're decoys.