The good news about this game is that all player, private, and custom match types count for each achievement, as long as you meet the gamertag requirement stated in the achievement text (5 or more in nearly all cases). In addition, any amount of gamertags signed in to splitscreen on the same Xbox count, but Guests do not. You can easily complete a session with only 2 people if you have 5 gamertags among you.
All that aside, the 500 kills can be gained easily using the Team Territory mode. When in the lobby, select the game type (the second option from the top) and then Create Custom Type. Set the options to the following:
Zone control: occupy
Then hit A button to save this type to Custom 01. Set the Time to 10 or 15 minutes, and place the guy whose turn it is alone on Gold team. Everyone else goes to Blue team.
When the match starts, the point that Blue team will spawn at is randomly selected, but is marked with a giant Blue box on the killer's screen. All the guy on Gold team must do now is move to the spawn area and camp just outside of it, and the enemy team will continue spawning inside the flares. Ideally, the cannon fodder will immediately fire their gun after spawning to disable the 5 second spawn shield, and the enemies always spawn facing in the same direction so it should be easy enough for the killer to find a safe spot to crouch/go prone to allow them to fire off a round.
Using Team Territory is much more beneficial than Team Elimination because there is no need for everyone to run to the guy on the opposite team following their semi-random spawns. Unfortunately, there is no way to force everyone to spawn faster than 10 seconds each death so the cannon fodder must hit A to spawn in the interest of time and efficiency. At the very least, the cannon fodder can turbo the A button which takes all of the work out of being gunned down.
Be aware that all manner of explosives do not seem to count toward this achievement. You must kill the enemy players with bullets.