WoWDB

I uploaded a screenshot that shows my method for achieving this. It's mostly the same as the video linked by velde046, but from the north side instead of the south side. It may be slightly easier since there were only three NPCs for me to keep track of instead of four (well, maybe three and a half, read on to understand).

Use raid markers to keep track of these NPCs - with all the other trainers running around and the many spinning blades, it's easy for the eyes to become fatigued and miss the important NPCs. I also put down both Rune of Power as a boundary marker so I would not accidentally wander out of the area and lose my progress. I didn't use smoke flares because they would obstruct my view.

Take a couple minutes to become familiar with the pattern of the marked NPCs. Every once in a while, the timing will be such that two (or all three if unlucky) will be bearing down on your position. The white path is the approximate emergency path that I would take when this would occur. When you use that path, you'll need to keep an eye out for the trainer that patrols that row. It's important to get back to your regular position as soon as possible!

Also, be comfortable with strafing movement (moving sideways). It allows you to react quicker.

Please note: The criterion will stay grey until the quest is turned in, thus you will not be awarded Ready For Raiding III (if you have the other criterion already) until you turn in the quest.

As of patch 5.1, the Shado-Pan Trainers now run much more closely to the pillars. (As such, the pillar trick no longer works.)

Patch 5.4: Now requires surviving for 60 seconds, down from 90. Quest reassigned to Yumi Goldenpaw.