I thought I'd go into detail since the other guide, while fine, doesn't explicitly get into how the ranking system works now. A side note, this achievement will be unlocked while you're working on the Spartan Officer and Lieutenant achievements.
So with the new EXP system, players are awarded 1 EXP for every game they win, or at least that's almost always the case. EXP is divided into two categories, your overall EXP and your playlist EXP. Your overall EXP from what I gather is basically irrelevant when it comes to unlocking the rank related achievements. Your playlist EXP is, as you might have figured, specific to individual playlists.
For example, if I have 3 EXP in the 7 on 7 playlist, and 14 EXP in the Social Slayer playlist, then my overall EXP will be at least 17. This achievement requires that you get 12 EXP in any one playlist. The other two more advanced versions of this achievement, require that you get 50 EXP in any one playlist.
The fastest, and easiest way to earn all three of these achievements is to get a group together from a boosting session. You will need at least eight people in your session to get this method to work. Gather your group, and go into the Rumble Pit playlist. As the matchmaker pulls up different games, veto anything that isn't Slayer.
Once the game starts, have everyone get two kills each, and then select one person to start killing everyone in the middle of the map, while all other players continuously respawn and go back to the middle to be killed again. Once the match is over, everyone in the game will be awarded 1 EXP.
Using this method you'll end up playing at most 50 games, but as long as everyone knows what they are doing, each game will only take about 3-4 minutes. Much quicker than trying to get these achievements naturally. Happy hunting, and good luck getting those achievements before they're gone!