Ok this is gonna sound rediculous, but it's an issue I'm sure everyone is familiar with by now.
I actually forgot what the "If They Came To Hear Me Beg" Achievement was for a long time and this morning on Co-Op Campaign I actually did it, but it wasn't from a fatal fall... it was near the two AA guns in The Package, nowhere near a high vantage point, with less than 35% health and the prone, "piggyback" assassination!
It was a face-off between myself and an Elite Captain when one of my team took down his shields, allowing me to sprint towards him once he turned around and trigger the assassination. This would suggest that the achievement itself hasn't shipped with the game properly and, in fact, can be done in a variety of ways.
[Edited on 08.31.2011 4:42 AM PDT]