Complete the indicated task to unlock the corresponding weapon. Most weapons are unlocked by buying them or earning them in Shooting Galleries - However, there's a few extra ones for completing certain tasks.

Deep Impact: Shoot ten grenades before killing Gregory to unlock his assault rifle.
Immolator: Shoot ten knives before defeating Major Evans during the first battle with him to unlock his handgun.
Twister: Complete the game to unlock Colonel Haynes' shotgun.
Volcano: Shoot down ten missiles before destroying the helicopter on Mt. Rosalia to unlock the Shadow Mercenary's rocket launcher.