Extermination

Extermination is a special medal awarded in Halo 3 Multiplayer for getting at least an overkill on the opposing team that results in the entire team being dead at once. It is represented by a gray cross with a red skull. This medal is only awarded if the entire opposing team is exterminated.

This medal is extremely difficult to earn, as you rarely find all of the same team together, and it is hard to stay alive killing at least four enemies within four seconds, each within those four seconds.

It is helpful to note that just getting an overkill on a four-on-four match in Matchmaking will not necessarily achieve the medal. This instance occurs often. In order to unlock the medal, you have to kill the entire team so fast that every member of the team is simultaneously dead for at least a moment. If any respawn before you get the overkill, you will not get the medal.

Perhaps the hardest conventional team slayer playlist to get this medal on would be Social Slayer, as it has a battle consisting of a five-on-five match. Excluding this, achieving this medal on Ranked Big Team Battle would be extremely noteworthy, because that would mean getting a Killapocalypse on the enemy team before any of them respawn.

This is most commonly received on Team SWAT, as you only have to get headshots, there is also a possibility of obtaining this in Grifball. Another easy way to get this is by obtaining the Rocket Launcher (or any other explosive weapon) and hope the other team is near each other in Ranked Team Slayer game, due to there being only four opponents, not five like in Social Slayer, but sometimes you can get this medal by luck using the Spartan Laser.
The easiest, however is to get an overkill in a 4v4 objective game, as the respawn time is longer. Also this is possible in big team but this is way more difficult due to the ammount of players.