It is possible to fall precisely 65 yards. Falling much further is fatal, however, except for rogues and druids, who have innate reduction of falling damage.
As a mage, one can [Ice Block] in mid-air and then continue.
A paladin can use [Divine Intervention] on another player that has just jumped, sacrificing themselves but allowing the target to fall safely.
What doesn't work
You must hit the ground, so falling into water does not apply, and neither does, as a Druid, falling the requisite distance and then shapeshifting into [Flight Form].
Priests' [Power Word: Shield] does not protect from falling damage, and neither does Dispersion.
Strategy
You and a friend go to a relativley flat and low-traffic area in either Outlands or Northrend. Terrace of Light in Shattarath works well for this. Both you and your friend need flying mounts that are the same size, otherwise, it's difficult to judge exactly where you are..
You and your friend fly up up a random height. You fly a little bit higher. You drop down. If you don't get it, your friend flies up a little higher and then you try again from the new height that your friend is at.
The more tries it takes, the less you fly up each time, as you know you're getting close.
Rinse and repeat until you get the achievement.
Easily identifiable locations
Leap off the prow of a zeppelin as it is coming into the towers at Undercity. This may be possible at other zeppelin towers as well, but Undercity is confirmed.
The elevator on its highest point of Scryer's Tier, you will need to fall on the floor, which is a bit lower than the bridge leading to Terrace of Light.
The elevator to Aldor Tier in Shattrath City. Stand at the forward edge of the platform as it descends, aimed straight for the Terrace of Light. The gap in the walls in front of the platform narrows to a point, then expands again. At the narrowest point, start running off the platform.
The north face of the top of the tower at Sunsail Anchorage onto the concrete below.
From the statue terrace in Stormwind Harbor onto the ground far below.
From the huge pipe in the sewer entrance of Undercity overlooking the War Quarter, walk into the sewer below.
Directly above the Auchindoun graveyard is a spire. Fly to the very top of it and land on it (it'll take a little effort to land on it). Then, simply walk off it.
In Exodar, fall or jump from the main descending walkway to the lowest level of the descending walkway around the main Naaru Crystal.
In Arathi Basin, jump off the cliff at the Lumber Mill.
Reach atleast level 40, aquire the Mechanostrider mount, while on the mount in Stormwind City, run towards the harbor, past the fountain to the left and fall all the way down to the bottom on the grass
Going Down?
[Divine Shield] or 
[Divine Protection] to avoid the damage.
[Ice Block] in mid-air and then continue.
[Divine Intervention] on another player that has just jumped, sacrificing themselves but allowing the target to fall safely.
