The Chronicles of Riddick: Assault on Dark Athena

For the quadruple kill it's easy with 2 players in the map Fate's Dam.Take the grenade launcher and stay on point.Aim the corner of the wall at right so that the grenade touches the opponent and raise or lower the point until he dies with a single grenade and repeat it until he says "massacre".The quadruple kill is yours.
Watch my video and good luck

Note there are three separate requirements to this achievement (listed in the description) and they DO NOT need to be done in the same round, though it is very easy to do so.

The 12X killstreak is challenging legit, but since nobody plays online anymore you should be able to get it with minor challenge. When the in-game announcer says "DEATH BY THE DOZEN," that's your 12X
(Get it? Dozen = 12)

The quadruple kill is, obviously done easiest with five people, but they should all weaken themselves down to single digit health, then whoever is getting the kill should use a rapid fire weapon, such as the assault rifle, SMG, or minigun. The timing window is very tight (roughly one second between kills), so make sure everyone is a good position to get shot.
The announcer won't say "QUAD KILL," but will say "MASSACRE" if you do it right. It can be done with fewer people but you have to get very lucky with spawn points.

And the FIRST and LAST kills are just that. The first kill is straightforward enough, and the last kill either has to be the game winning kill, or the last kill made before time expires. They both need to be done in the same round though.