Cannonballer

As of Warlords of Draenor, this achievement is much easier to get.

First, to queue for a Mists of Pandaria scenario solo, go to the top of Mogu'shan Palace in the Vale of Eternal Blossoms (if you have flying), or speak to Mishi, the small flying serpent at the base of Shrine of Two Moons/Shrine of Seven Stars (bottom floor) to have him fly you to the top of Mogu'shan palace - this is where the archaeology/Lorewalkers NPCs are.

[npc=78709] is the solo scenario queue NPC. Talk to him and click "Tell me of how Varian and Tyrande learned a Little Patience" - which essentially queues you for the scenario.

At this point, you can look for the defenses you need. The way to do that right at the start is to look for the proper NPCs on your map - the defenses will show up as two speech bubbles on the map (it takes about 10-15 seconds after the start of the scenario for them to show up).
[npc=67883] - Gnomish defense, grants Which Came First?
[npc=68599] - Night Elf defense, grants I Used To Love Them
[npc=68057] - Dwarf defense, grants Cannonballer
[npc=67569] - Jinyu defense, grants Bubbletrapped!
[npc=68240] - Pandaren defense, grants We've Been Dancin'

If the two that randomly spawn aren't the ones you need, simply leave the instance and queue again.
The next instance will have 2 random new defenses active (which may be repeats, given RNG, or different). This can be done over and over without a penalty, so you just keep leaving and re-queuing to get all five achievements! Keep in mind that as soon as the defense is complete, you get the achievement - therefore you can leave and re-queue as soon as that happens.

Each time you do battle in the A Little Patience scenario, you will be aiding 2 encampments, randomly chosen for you. If you truely do have the patience to do this scenario multiple times, you will eventually complete the following achievements for helping out each of the different encampments.

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• Bubbletrapped! for helping the Jinyu
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• Cannonballer for helping the Dwarves
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• Which Came First for helping the Gnomes
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• I Used to Love Them for helping the Night Elves
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• We've Been Dancing for helping the Pandaren
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For those who like references, it seems all of these relate to songs by the band Guns 'N Roses.

Nevermind, I guess its random. But try opening up a toolbox that is closer to the camp that you want selected as soon as the scenario begins. This seems to increase the chances that you will get this camp in my opinion because before I did that, all I ever kept getting was the Night Elf and Pandaren camps.