You earn this trophy in the Eridium Blight area.
Donkey Mong is a rare spawning enemy that will appear near Ore Chasm. He is not to be confused with King Mong near Heroes Pass.
You will notice large barrels on his back that he throws at you, and of course his name is Donkey Mong.
I found the best way to get him to spawn is to enter Ore Chasm, come back to Eridium Blight, run left and see if he has spawned. If not, run back to Ore Chasm and repeat.
You don't require killing any additional enemies to make him spawn, he is simply there, or he isn't. Also, if you kill him or another player kills him, everyone gets the trophy.