DOOM + DOOM II

If you are doing this on Xbox, you will need to plug in a keyboard to be able to type in cheats

Load up Doom 1, select E2 "The Shores of Hell" keep it on Hurt Me Plenty difficulty (or you can do it on a harder difficulty)

When you spawn, type in "IDKFA" to get max ammo on all weapons, Select the Plasma Rifle and take the first right, you will see a group of Former Human enemies and just shoot them all, the achievement will pop when you kill the 5th enemy

For those who aren't using cheats, here's a quick and easy way to get this achievement.

Game: Doom
Level : E2M1 - Deimos Anomaly
Difficulty : Hurt Me Plenty (any less a difficulty and there won't be enough enemies)

From the start of the level, jump through the teleporter ahead of you, grab the shotgun and work your way around to the right clearing enemies until you reach a bridge across lava. On the other side of the bridge is a switch on the wall. Hit it and then on the panel that came out of the floor, hit the button that is furthest away from the wall. Head back across the lava and work your way back around to the left to the teleporter then jump through.

There are a lot of grunts milling around and they can in-fight so the next bit has to be done fairly quickly.

Run through the upside-down cross and enter the teleporter to the left of the blue key card.

Immediately run to the right, grab the plasma gun and then get back through the teleport. Don't bother engaging any of the enemies here.

Run back through the cross and (hopefully) there'll be enough grunts left to easily get the 5 kills needed for the achievement!

All credit to aperfecttool72 who posted this as a comment, it's by far the easiest solution:

Game: No Rest For The Living

Level 8: Tomb of Malevolance

Difficulty: I'm Too Young To Die

"After you spawn in the first room (no enemies here on this difficulty), go right and look at the two bloody windows to your right. The one of the left is a secret room.

Click the skull switch and turn around 180. The wall on the right has opened and the plasma rifle is at the top of the stairs. Drop off after getting the map and head to the main demon face door.

Get the mega armor and go through either door. Collect the rocket launcher and rockets before activating the skull switch.

Save just in case

Switch to the plasma rifle and hit the switch. The floor will lower down and there is a big group of Imps here. Melt them down and you should get the achievement!"

If you are doing this on Xbox, you will need to plug in a keyboard to be able to type in cheats

Load up Doom 1, select E2 "The Shores of Hell" keep it on Hurt Me Plenty difficulty (or you can do it on a harder difficulty)

When you spawn, type in "IDKFA" to get max ammo on all weapons, Select the Plasma Rifle and take the first right, you will see a group of Former Human enemies and just shoo them all, the achievement will pop when you kill the 5th enemy

Doom 1, E2M1 Ultra-Violence
IDKFA for full inventory
Weapon 6, take the first right and toast the fools.