Here are the current minimum kill requirements for shotguns in Black Ops 2 Zombies. This assumes that you have a high Kills Per Down as you reach each milestone to rank up:
5,000 Kills - Skull
15,000 Kills - Skull and Knife
30,000 Kills - Shotguns
Assuming that you have the required KD at each of these kill milestones then you will get the designated rank. Problem is, nobody knows for sure the exact kills per down you require to achieve each rank.
If you don't know how to determine your KD, take a look at your CO-OP stats (not career, those include versus which doesn't contribute to your ranking), and divide Kills by Downs. Don't worry about deaths, just kills and downs. There's a lot of confusion on the forums because people say their KD is their career kills divided by career downs. This gives an incredibly inaccurate look at how the ranking system works and is why people still don't get it!
The way I see it, you should just become so good that your KD is way beyond the requirements for shotguns. At that point, you deserve the shotguns anyway right? So I created a new account to test my theory. At 5,000 kills I checked mid game and saw that I had become the Skull emblem (you press select then Y to view your gamer card). At 15,000 Kills I also checked mid game at exactly 15,000 to make sure I had become a Skull and Knife. Same story for 30,000, my gamer card updated (though score screen didn't show until the game ended and I returned to the main lobby).
I had a 600-700 Kill to Death ratio the entire time, so I knew I was way beyond the requirements for each rank. My guess is that you need 200+ Kills Per Down in order to achieve the Shotgun rank and the game only checks for it every X Kills. Probably every 5,000 or so kills past 30,000 the game will see if you've passed 200 KD yet. If you have then you get the shotguns.
I played every game until I died, not that I think it matters. I also don't think you have to get high rounds. I played all public or solo on normal mode, no custom easy games.
On the leaderboards people see round, kills, downs, headshots, and revives so they assume those are key to ranking up. No, all that matters is your kill to downs. I even used the ray gun and mustang/sally to ensure that my headshots were absurdly low, proving that those aren't required either. My accuracy was out of this world, like 4+ lol, but I don't think that matters either.