Bulletstorm

This achievement requires you to quickly kill enemies on different floors as you go up in a lift. I recommend the boneduster and the flailgun.

When you reach the lift, prepare a charged shot on your boneduster.

(EDIT: Also make sure you kill all the enemies in the room before entering the lift. People have said that this is required for the achievement to unlock.)

Once the lift starts, your first 2 enemies will be directly ahead, shoot them quickly with the charged boneduster.

Now keep pressing to charge your boneduster again and turn 90 degrees to the right where you will see 3 more enemies. Shoot them quick.

Now switch to your flailgun and turn 90 degrees to the right again. Fire 2 shots quickly and detonate them fast or you may miss these enemies.

And last of all, turn 90 degrees to the left and shoot at the last enemy.

The achievement will pop when the timer on the top floor reaches 20.

I have uploaded the video below so you can see what to do for the achievement:

EDIT2: If you feel the need to down vote my solutions, please tell me why in the comment section so I can fix the solution, or see that you are just some sado down voting solutions for the sake of it.
If you voted up, thank you :)

Once you get to the point where you need to press X to "Drop Down", drop and kill all enemies before the lift (It doesn't say you need to in the achievement description, but these enemies count).

Enter the elevator. While riding up the elevator, there will be four groups of enemies. The first group will be at the back, the second will be to the right, the third at the entrance, and the fourth to the right.

Use your Thumper on the second and third groups. Then, for good measure, aim down and use you last Thump.

You'll get a bunch of ten point kills, Vertigos, and Flyswatters. The achievement should pop when you reach the top floor.

Everyone listen up! I just got my achievement and can probaly fix it for all of you. You need to kill all the enemies in the room w/ the Elevator. This is before going up. The achievement says "Whilst Riding the Elevator" but it's wrong. You must kill the enemies before getting on. I played this for over ten hours thinking I was permanetly glitched. I missed the very last enemy when you're going up the lift and got it anyway. Also make sure you wait until the counter (on the final floor) is below 20. This is when the achievement will pop if it is going to.

First of all I have seen a youtube video with someone getting this achievement. I haven't gotten it yet but I believe it is glitched for me and maybe others. I have done it successfully at least five times with no achievement popping up yet.
On the level you will get to a part with an elevator. I used a shotgun and flail gun to get all of my kills. Have them both charged before you hit the button.
The first level will have two guys. I used the charged shotgun to kill them easily.
Quickly restart the charged shotgunn and kill the three green guys as you pass them on the second level.
The third level has between 5 and 6 guys, I have seen both. I used the shotgun power on them again. I have had friends used the charged flail gun here too and the thumper has worked as well.
The last level has just one guy and you can kill him anyway, I used a normal flail gun shot.
You should get the achievement before you leave the elevator, but like I said I have done it a couple times with no luck. If anybody else has some advice let me know and I will add it here

EDIT- I finally did get it so keep trying and you will get it eventually