You don't have to worry about killing every enemy you see with Killmonger, but it doesn't hurt. The reason is that in the final stage, both the Black Knight and Klaw will send waves of enemies at you and you must kill a certain number of them to progress. There are far more than 20 enemies between these two encounters.
On the plus side, any buddy attack kills you do by pressing
near your partner count toward this achievement as long as you control Killmonger. So let the enemies gather up and then do a buddy attack to clear them quickly.