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.

Summary
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 of each other.

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 doesn't occur 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 Slayer, as it has a battle consisting of a four-on-four match. Excluding this, achieving this medal on Ranked Big Team Battle would be extremely noteworthy, because that would mean getting a Killtastrophe on the enemy team before any of them respawn.

A fact about the Extermination medal is that you don't have to kill the whole team, as long as they're all dead. ex: You get an Overkill in a 5v5 match, and the other player is on the respawn; as long as all players are on the respawn, and you receive an Overkill and the Extermination, whether you were the one who killed the whole team or not, which can be useful in Big Team battles. Inversely, you can also get the medal in a 2v2 match by killing both enemies twice, and spacing out the first 3 kills.

This is commonly received on Team SWAT, as you only have to get headshots, where it is very easy to obtain on Snowbound due to the fact that all the opposing team members will be close to one another. It is also more easily obtainable in Grifball, another easier way is to get an overkill in a 4v4 objective game, as the respawn time is longer. 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 a Ranked Team Slayer game or in social slayer.

It can also be obtained by killing the person who is in a team consisting only of himself, four times within four seconds of each kill.

Another way to obtain this medal is to be on a 2 flag CTF on Snowbound. Get the Beam Rifle and find some cover, with a good sniper view. Once your team grabs the flag, get ready. It is likely the entire enemy team will be after the flag carrier, so if you manage to get a 4-5 multiple kill with the Beam Rifle, you will get the medal.