Once you have started the mission, it is actually very short. All we really need to do is head to the Troop Bushido base, located at the objective marker in Little Tokyo.
As you arrive, run up to the door and interact with it. Then, jump up to the roof and interact with the window for a scene. This will introduce a new faction for you to do missions for whilst also completing the mission.
|$ 1,500||Fast Travel: Troop Bushido Base|
|2,000 x Overcharge|
|Clothing: Troop Member Vest|