Donkey Mong is a Bullymong boss in Borderlands 2.
This boss is an Easter Egg, a reference to the video game "Donkey Kong"
Just like the original Donkey Kong, Donkey Mong throws barrels at you.
How to find Donkey Mong
Donkey Mong is a rare spawn in the Eridium Blight, along the south border between the exits to Hero's Pass and Ore Chasm. Patrol the area with a Light Runner and if you don't find him, log out of the game and then try again, repeat until Donkey Mong spawns.
Achievements - Trophies
Achievement Bugs and Glitches
The Definitely An Italian Plumber achievement is not known to be bugged or glitched.
The most common reason for which you have no achievement is that you killed King Mong instead of Donkey Mong. While their names are similar, killing King Mong does not give you any achievements or trophies.