BB King

To try to help someone who wants to complete this achievement as of patch 5.3, I shall try to summarise a lot of what has been said.

Tips: These are boss level NPC's, so there's a good chance you will miss once or twice - particularly if you elect to try the 'naked' approach and have no hit.
- Keybinding your rifle will help to get a few shots off in quick succession while you're in the process of dying.
- Don't stand too close to the boss, you need to be outside melee range for the rifle to work.*
- The rifle has a one second cast time, taking damage during the cast will delay getting off a successful shot.
- Doing this with two or more players makes it a lot easier. After your initial deaths, the other player(s) rez first and draw aggro while you get several shots in without interruption.
- Expect a hefty repair bill.

So, to get the achievement;

1. Purchase a [item=46725] from a toy vendor in Stormwind ([npc=52358]) or Dalaran ([npc=29478] and [npc=29716])
2. Don't forget to purchase the ammo ([item=48601]) for the Rifle (Wowhead incorrectly lists it as not available to players)
3. Fly to the appropriate Horde city for your target and proceed as follows;

Garrosh Hellscream
Hover above his headquarters (location 48.2 / 70.6) in Orgrimmar and locate the entrance on the South Eastern corner of the building.
Fly directly into the entrance, as you enter you will need to navigate around a small wall blocking the entrance and into the main hall. Garrosh will be on a throne directly opposite you as you enter. You will immediately start getting attacked by NPC's. Target Garrosh and fire your rifle. You will die.
If you didn't get credit (see tips above), corpse rez and try again.

[npc=36648]
Fly to the tallest totem in the middle of Thunder Bluff and land on it.
Turn to face east and you will see a long red roofed building below you. In the entrance, at location 59.8 / 51.6, you will be able to target Bain Bloodhoof before you fly into combat. Fly down to the middle of the clear area facing him and get a few shots off before you die.
As before, if you didn't get credit, corpse rez and try again.
Tip: If you're not familiar with this zone, it can be a pain in the butt finding you way back to your corpse to try again, so take a few minutes flying around to work out which lift you will use and roughly how you will find your way back.

[npc=16802]

Firstly either take the flightmaster ride to Zul'Aman in Ghostlands, or fly to the top of Eastern Plaguelands and ride through to Ghostlands. From there ride to the entrance to Silvermoon City. Take a moment to look up the map of Silvermoon City (Burning Crusade). You will need to make your way from the entrance to the northwestern corner of Sunfury Spire.

There's no quick way to do this that I'm aware of. You will just need to run in and try to pull as little aggro as possible. You will have to deal with various NPC's up to and including level 90 (obviously, if your class can stealth, do so. I did this on a level 85 human warrior, so didn't have that luxury).
Probably the simplest and quickest route is to head north from the entrance towards Murder Row. Then from there to Court of the Sun, watch for the level 85 pats alternating on either side of the fountain. As you go up the ramp to Sunfury Spire, you will see two rows of level 85 NPC's. If you can stealth, great. If not, you can try invisibility potion. If not, then kill them all - dying a few times in the process.
Finally, you will be able to make your way to the courtroom. Lor'themar is in the northwestern corner. Usual story, target, shoot, die. Corpse rez and repeat until you get credit.
If you encounter too many Horde players during the run, it's probably worth waiting for a quieter time on your server and trying again.

[npc=10181]

Fly to the entrance to the sewer at location 51.0 / 71.6 on the Tirisfal Glades map. If you don't have location finder, it's on the map as a tunnel entrance on the eastern side of the range of hills located underneath the 'O' and 'L' of Cold Hearth Manor.
Fly in to sewer and take the right hand (smaller) entryway when you get to the first chamber. Dismount and follow the hallway through a series of right and left turns until you find yourself in the main body of Undercity (I found no NPC's up to this point). You can now mount up and fly again.
Turn right and fly along the wall until you see a large series of steps leading into tall entrance you can fly into. Its in the Apothecarium Quarter at location 52.1 / 63.9 (or under the 'E' in Apothecarium on the map if you don't have location finder). You can fly all the way down the hall that leads to the chamber with Lady Sylvanas. Once in there, she's on a raised section in the middle of the room, surrounded by NPC's.
Target, land, shoot, die, corpse rez, try again until you get it. With this one it definitely helps to have another player rez and draw aggro before you try as the mobs pat very close to Lady Sylvanas.
This map showing the location of [npc=10181] is useful to help you work out where to go once you're inside the sewer.

A thought that occurred to me after I completed this achievement, is that some of these Horde leaders exist in several different locations in the game. It's possible that you could pelt the leaders in much easier locations than their home cities and get credit for it. I'd be very interested if someone tries it and gets the achievement, to hear about it.

Have fun, and good luck.

*Thanks to Soulwrencher for pointing out that it doesn't work in melee range and you'll get a 'target too close' message.

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This achievement is not a requirement for the Merrymaker meta-achievement.

You'll shoot your eye out, kid.