This achievement can only be earned on the eleventh story chapter, Helm's Deep.
In the level Helm's Deep in story mode, you'll have Gimli, Legolas, and Aragorn as playable characters, which works perfectly for this achievement. Don't use Aragorn as he has no use here.
In the level, the attacking Urak-Hai take two hits to be killed. The first hit eliminates their armor, while the second deals the killing blow. To get the achievement, deal the first strike on an enemy as Gimli, and then finish them off with Legolas.
The achievement doesn't seem to unlock a lot of the time, and I didn't get it right away. If you are following the above instructions with no luck, simply consistently alternate as Gimli and Legolas while fighting Urak-Hai and the achievement will unlock before too long. If you don't get the achievement on your first story mode playthrough, replay the level and try again. It seems to unlock more if the two hits by both characters are done in quick succession, so doing this in co-op will prove easier because of not needing to switch characters for each hit. You can simply have your buddy be Gimli and strike immediately after, and then he can take a turn being Legolas to get the achievement himself.