If anyone's still trying to get this achievement, I have some tips for you.
1.Do it on Pillar of Autumn (that beginning partwith the cliff, sprinting IS ok)
2.The game dosen't register that the fall will kill you until you hit the ground, so you have to assassinste the elite in that fraction of a second time frame while it's computing the damage done.
3.Celebrate once the achievement is obtained.
I hope this helped
P.S. If you do the air to land animation (jumping on it's neck) you WILL NOT get the achievement