Bounce

At first, this seemed to be completly uncontrolable, but in fact, this is not too hard when done right.
While still in mid-air, turn your charakter (using your mouse of course!) to face the center of the trampoline, and press your move-forward button and/or both mouse buttons. Remember, you don't have to hit the "bounce spot" at once, you have a very short grace period during which you can move towards it without resetting the counter (to show the counter, simply track the achievement), so keep your forward button pressed while landing and immediately move to the center of the trampoline.
While this still involves a certain degree of luck, you are much more likely to stay on the trampoline that way.
Good luck.

Edit: Some people found it easier to do this while being mounted. So, if you have any difficulties to reach the "bounce spot" in time, try to use a ground or flying mount for this. Personally, I preferred to do this without a mount, but hey - whatever floats your boat :)

Also, this achievement is currently bugged. After you complete the quest Aessina's Miracle, it seems to be impossible to make more than one consecutive bounce. Apparently, this issue is fixed on the patch 4.0.6 PTR.

Here's how I did it and what I found,

As suggested this is indeed easier whilst on your *ground* mount. I tried with a flying mount and found that sometimes it would not land and I would miss the jump.

To gain the achievement you must be roughly in the center of the trampoline each time the bounce happens (you will see a small dust blast when it does.) You must do this 20 times in a row.

If you miss the bounce (dust blast happens before you're in place) the counter resets.

The best way to do this is on a ground mount. Why? Because you will need that extra speed to get to the center of the trampoline before the next blast.

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• Mount up and move to roughly the center of the trampoline. Set your camera for a bird's eye view looking directly down on yourself, this will help you orient.
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• When the first bounce happens look at the direction you move (Tip: You will bounce in the direction that you last moved. So if you moved forward you will bounce forward. If you strafed left you will bounce left. This becomes random after one bounce so long as you do not move again.)
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• Spin around so that you face the center of the trampoline again. When you land immediately run towards the center. If you did not bounce that far then move only slightly so that you'll be propelled forward on the next bounce.
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• Repeat this until you have your achievement!
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A few notes:

Occasionally you may find that you've missed your bounce for no apparent reason. This may be a bug. I found it happened more often when the trampoline was crowded (5+ people on it at the same time.)

A bounce blast occurs for each player on the trampoline. If there are multiple people on the trampoline don't worry, your bounce won't occur until after your feet have touched the ground.

Taking damage will not reset your bounce counter, if you take damage that's fine just make sure you get to the center of the trampoline before the next bounce.

I recommend tracking this achievement whilst attempting it. Seeing the counter lets you know if you're doing it right or wrong.

The trampoline is located in Hyjal at location 13, 33. I tried the dragon, and just my character, but my mammoth is what made it super easy. Try it out :) first try done!