Malfeasance is an Exotic hand cannon available for the new Gambit mode in Destiny 2. Its perk, Explosive Shadow, will explode inside the enemy after five rounds. A nice bonus is that if you've got two players using Malfeasance, it counts both of your shots against the total needed to cause the explosion. If you want to get ahead in the new Gambit mode, this gun will be your ticket, as you will do bonus damage while fighting both Gambit and Taken invaders.
The process of getting the Malfeasance is a rather short and sweet one, as compared to other exotic weapons. Getting the quest started, however, is a brutal process that boils down to luck and timing.
Step 1: Ascendant Primeval Servitor
First, you need a special boss to spawn. Welcome to the RNG portion of the quest. Instead of Primeval, it'll be the floating meatball from the end of the Forsaken campaign, the "Ascendant Primeval Servitor". He could spawn at your first Gambit match, or you could grind for 8 hours and won't see him once. It is totally random so be prepared for the worst and hope for the best. He seems to only spawn when you have a chance of winning the match, so it looks like he won't ever spawn on the first match.
Once he spawns, kill him. Kill the envoy's first, which will take down the Primeval's stacks. Save your supers and other resources until after the first few invasions, and once you're in melt mode - then go in for the kill on the Primeval. If you're melting Primeval and he's just about to die, ignore the invasion and continue killing. Don't get into position for the invader, in positions easy to pick off.
