DOOM + DOOM II

if you are doing this on Xbox you will need to plug in a keyboard to type in cheats

Load up Doom 1, select any difficulty as we will be using God Mode cheats (I left it on "Hurt Me Plenty"

Type in "IDCLEV48" when you spawn in and it'll take you to the final level
Type in "IDDQD" for God Mode (invulnerability)
Type in "IDKFA" for max ammo on all weapons
Type in "IDCLIP" to be able to clip (walk) through walls

When you have all cheats activated, walk down the stairs in front of you, through the big door, keep walking forward and through the centre (you will see Cacodemons around you) keep walking and you will see a door a bit above you and a gap, just keep walking as you will Clip through the wall and land on the other side. clip through the door in front of you and you should see the Spider Mastermind when you enter the room. Use any weapon on it (a few BFG shots will drop it quicker) when it is dead the pillar in the middle will start to drop down and reveal an orange Portal, you have to deactivate NoClip mode to be able to get through it, simply type in "IDCLIP" again to turn it off and drop through the Portal, achievement should pop soon after

Requires a plug-in keyboard for Xbox.

Type in "IDCLEV48", you will be warped to the final level.

Then type IDDQD (invulnerability) and IDKFA (all weapons and keys)

Go forward, press the button on the wall to the right to open the door and head for the column in the center. Go to the locked walls on the sides and unlock them with the keys. Kill the cacodemons inside and press the buttons to open the bride to the final boss. Kill the Spider Mastermind and jump into the portal which opens in the center of the large room.

You could also no-clip this, someone please confirm this.

If this solution is out-of-date, let me know before voting negative.

If (like me) you have an Xbox but no keyboard, you can just select the level in the level select options. You don't need to play through any other level of Doom. Only the very last one counts for the achievement.

Single Player > Level Select > Episode Thy Flesh Consumed > Level E4M8: Unto the Cruel
Difficulty: I'm Too Young To Die

Grab the shotgun, run down the stairs and go through the door. Run around to the left, open the wall with the demon symbol on it and jump into the teleporter. In the open area grab the plasma gun by the wall and then head up the steps. Follow the path around to the left until you enter a room with a switch on the wall and a lift on the floor. Press the switch and go down and grab the yellow skull key. Follow the corridor around and jump into the teleporter.

Back at the start area, this time run around to the right and open up the demon wall and grab the red skull key. On the middle platform open the red door and yellow door and press the buttons. This will make a ledge appear and steps rise up to a door.

Go through the door and kill the Spiderdemon then jump into the hole.

Achievement earned!