Gears of War

This is the fastest way I got the achievement, if you have two controllers, go into a local match for Process and choose whichever side you want. Set aside the controller that is going to get this achievement. The other controller will be the one you will be committing suicide with.

If you start in front of the stairs, go forward just a bit and go right down the stairs, there will be grenades there, toss one at the wall and die.

If you start in front of the bridges, go forward and hang a left, you will see three barrels in close proximity and grenades just in front of those, toss a grenade at the barrels and die.

The whole process, including intermission, should take 1min 40sec if done right. Enjoy your achievement when you get it.

An even quicker way to get all the ''play 20 matches dlc map' achievements'' is to start an assassination game with friendly fire turned on. There should be atleast 2 players who should get the achievement and have 2 guest account's on the other team who will kill their own leader. With the leader dead the round ends and the other team wins. Repeat this 19 times on the required map and you should get the achievement. Me and 3 other friends were able to get each of these achievements in 15-20 mins

Just an optimization of the two controllers method:

Set the profile you want the achievement to get to the Locust side.
Round 1: COG runs for the grenades just a bit right when you run up the stairs, and commits suicide (~ 20 seconds)
Round 2: Locust runs for the longshot behind the barrels and kills COG without getting close to him (~ 30 seconds)
Round 3: COG commits suicide again as in round 1.

The whole match will last around 1:30 + loading times but still less than 2 minutes. Achievement pops after less than 40 minutes.

This achievement can be had with two controllers in a local or system link game, just like the other achievements in the Hidden Fronts pack. I know, because that's how I did it.

EDIT: I presume I am getting negative feedback because IdeaLista82's solution is better, but for the calendar-challenged among you, let me remind you that my solution was posted well before his.
p.s. IdeaLista82's solution is excellent (I assume. I haven't tried it since I already have the achievement).