As described, use Zetterburn's Aerial Down Special to KO an opponent, but I ran into two additional factors:
1) your opponent must also be in the air when you hit them and shouldn't hit the ground after.
2) if you die during this maneuver, you'll only get the achievement if the opponent's death actually registers. So either the opponent dies first or you have additional stocks to respawn with after.
In the instance I got it, I died seconds before the CPU (it tried to recover but failed), but we both had a remaining stock to respawn and I got the achievement. In a try where the achievement did not pop, I died first and lost my last stock, so the game ended before registering the opponent's death (it was just off screen but not yet dead).
I personally did this in local versus with a lvl 1 CPU, though should be doable in Abyss mode or against a willing friend.
For CPUs, try to bait them towards the edge. Sometimes I had to knock them off myself, then quickly try to strike them before they recovered.