Tol Barad Saboteur

You can actually solo this achievement if you got both a Horde and an Alliance toon.

If you want to do the achievement on your Alliance char, wait til Alliance controls Tol Barad. If on your Horde char, wait til Horde controls it. If you don't care, even better.
I will explain it in case you want to get the achievement on Alliance, of course you can simply swap otherwise.

1) Alliance controls Tol Barad. So Alliance defends, Horde attacks.
2) Park your Horde char near the northern bridge at the entrance.
3) Remove your gear at your Alliance char and wait til the next match starts.
4) Alliance will get ported to the center. Mount up and get to the bridge to engage the Horde NPC guards there.
5) Alt + F4 while in combat.
6) Log in with your Horde char and kill your Alliance char who should still be in battle with the guard.
7) Your Horde char can now mount siege engines! Grab one of the northwestern ones and drive it to the northwestern tower to deploy it there.
8) Mount up and move as quickly as possible to the southern group of siege engines. Get in one and deploy it at the southern tower.
9) Repeat at the northeastern tower.
10) Alt + F4 and log in with your (dead) Alliance char.
11) Wait til he's resurrected, mount up and get to the northwestern tower, put your gear back on.
12) Kill the siege engine there.
13) Proceed to southern and northeastern tower.
14) If your damage is decent, you should be able to destroy all 3 siege engines before one of the towers gets destroyed.
15) Since you were alive and actively destroying them, you will get 6 points for the achievement (being alive directly beneath a siege engine that gets destroyed gives 2 points instead of 1).
16) To get your 20/20, you have to repeat this process a few times. Of course it's much faster if you can simply bring a friend, because you can destroy them while he deploys the next and so on, but if not - this should also work fine.

If you are unable to see your other char in battle, remember that war mode on / off gets you to different instances of Tol Barad. This can be useful to find an instance that is controlled by the faction of your wish or simply to find another battle instead of waiting 60 minutes.

Since there seems to be some confusion as to whether this achievement is bugged or not:

When a siege engine is attacking a tower, there is a vehicle button option "Deploy Siege Engine." Once this is used, the player controlling the engine is ejected from it, and the vehicle begins attacking the tower autonomously. This is the engine that needs to be destroyed to get credit for the achievement. Killing the Siege Engine BEFORE it is attacking the tower will not gain any progress with the achievement. Hope that helps.

The attacking team member must get one kill first in order to get into the siege engine. Once in range of a tower, the deploy button will work.