Credit goes to the first author for listing the game modes/types and to Catatonic Nali for detailing that the games can't be "Custom". Thanks guys.
As I've just gotten this achievement, I went ahead and created an amended solution with some detail on how long the matches take, what the matches are, etc.
Every game must have at least five unique gamertags in it to count. I wouldn’t have more than six people total because if you have more than that, the Solo games are going to take that much longer (you figure, for one person, they take 35-40 minutes. Multiply that by the amount of people in your session… the fewer, the better).
EDIT - It has been noted by Mental Jay that if you already have five unique gamertags, you *can* use a guest account as a sixth tag and place them on the other team by themselves so you only have to go through the Team game modes one time. This will cut the time in half!
Consequentally, you can also use a second console/game/profile as well and do the same thing by putting this extra profile on a team all by itself. Again, unless you need the second console as a fifth gamertag, I would really only use it for the Team games.
You can't change any of the Game Type settings, like Respawns or Enemy Density, as the game will automatically switch to "Custom". This will void the achievement. As long as the Game Type box in the lobby doesn't say "Custom" you are good.
Basically just choose the default game mode and game type (listed below). Do NOT “Create Custom Type” at all. Just choose the game types that are already created. You CAN change “Advanced Settings” (see below) as this does not change the ‘Type’.
Create an Xbox Live party so everyone can communicate. It’s also easier to invite the entire party from there because there are still randoms playing this game (believe it or not). In the “Advanced Settings”, set the “Number of Players” to however many people are going to be in your session so no randoms can join and ruin your fun.
These can be done on any original map. I recommend Desert Gulch since it is the smallest.
Setting up your game:
Xbox Live > Player Match > Create Public Match
Map: Desert Gulch
Time: 5 Minutes (for some game types I would change this [see below], but the default should be 5 minutes)
Advanced Settings (these are the only ones you need to change):
Number of Players: 6 (or however many players are in your session, really should be no more than 6)
Method for Player Assignment: Player Control (so each player can change their team if necessary)
Team Start Location: Standard
Game Start Timer: Off
Map Rotation: Same
Map Plays: 1
Press Y to host and when the lobby opens up, invite your party immediately. Everyone accept as quickly as possible to avoid randoms joining.
The original game modes & types (there are 20 total) are as follows:
Note: Team games should take around 35-40 minutes total per team, times two teams, so around 1.5 hours total (that is, if you don't use a guest account, although I recommend you do to save time)
• Team Elimination: Last Man Standing (quick, everyone on the losing team commits suicide with a grenade [no respawns])
• Team Elimination: Sharpshooter (requires 50 points [kills] - set the time limit to 10 minutes for this game. Have the losing team just run to the middle to be killed)
• Team Territory: Siege (quick, everyone on the losing team commits suicide with a grenade [no respawns])
• Team Territory: Domination (ends with a 5 minute time limit)
• Team Territory: Hamburger Hill (ends with a 5 minute time limit)
• Team Objective: CTF (requires 10 points [flag captures] - set the time limit to 10 minutes for this game) - Standard CTF boosting… for this game type, the flags are at the teams’ spawn point
• Team Objective: Recovery (requires 10 points [flag captures]) - Standard CTF boosting… for this game type, the flag in the center of the map, not at each teams’ spawn point.
• Team Objective: Search and Rescue (ends with a 5 minute time limit - to “capture” the three officers, no one on the winning team should be standing in the capture area. The officers won’t enter if there are players in there)
Note: Co-op should take 8 minutes tops (since everyone is on the same team)
• Co-op Elimination: Firefight (kill all A.I., default is Medium Density [40 enemies], 2.5 minutes tops)
• Co-op Territory: Defend (kill all A.I., default is Medium Density [40 enemies], 2.5 minutes tops)
• Co-op Objective: Recon (kill all A.I., default is Medium Density [40 enemies], 2.5 minutes tops)
Note: Campaign should take no more than 15 minutes (since everyone is on the same team)
• Campaign: Mission (Co-op 1-1 through 1-4, NOT Single Player) (set the time limit to 30 minutes just in case) - Old Town is the easiest map, just be cautious and careful. Use cover, don’t run out in the open and USE YOUR DRONE (Back button, aim where you want your drone to go, then press Up on the D-Pad).
Note: Solo matches should take around 35-40 minutes total for each gamertag
• Solo Elimination: Seek & Destroy (ends with a 5 minute time limit)
• Solo Elimination: Thief (requires 15 kills to end - set the time limit to 10 minutes for this game)
• Solo Elimination: Sharpshooter (ends with a 5 minute time limit)
• Solo Elimination: Bounty Hunter (ends with a5 minute time limit)
• Solo Elimination: Last Man Standing (quick, everyone losing commits suicide with a grenade)
• Solo Territory: Hamburger Hill (requires 150 points, 1.5 minutes worth) - King of the Hill basically
• Solo Objective: Escort (requires 50 points, 1.5 minutes worth) - Just run into the officer and he will follow you around
• Solo Objective: Flag Carry (ends with a 5 minute time limit)
If you feel the need to down vote this solution, please say why. I think that this is 100% accurate (as my session got this achievement using this solution) and it gives exactly what you need to do to unlock this achievement.