In Mission 04, after defeating the Shadow, go to the room with the airplane and ride the elevator down again to activate this Secret Mission. There is only one shot at this, so if you fail and want to complete this mission, don't save. It's unfortunate but you'll have to reload your previous save.
Preparation is key. Purchasing Air Raid, Stinger, an Untouchable, and a few Blue and Purple Orbs are all highly recommended.
All you have to do is fight three Shadows and survive. Focus on defense, and take pot shots at them with whatever firearm you like until one reveals its core, then do your best to melee that one while dodging the others. Using Devil Trigger will help prevent the other Shadows from interrupting your attacks and will ramp up your damage, but watch your health and always stay on the defensive.
One strategy to defeat them was to walk in with Ebony and Ivory, wait for their ranged shadow spike attacks, enable Devil Trigger and blast away as rapidly as possible. They're stuck while they're "spiked" and you do a nice chunk of damage. Using Devil Trigger while slashing away at them is also a good idea so determine your best approach. The above information is still absolutely critical.
Before starting this mission, take out Phantom and as he's dying, keep taunting his corpse to rebuild Devil Trigger.