Complete the following tasks to unlock Vita trophy rewards.

Trophy	How to unlock
A For Effort (Silver)	Complete Mission 4 - Marathon.
A Real Weapon (Bronze)	Upgrade your melee weapon again!
And Back Again (Silver)	Complete new game+.
Armed And Ready (Bronze)	Acquire the pistol.
Autodefenestration (Silver)	Complete Mission 7 - Beauty And The Beast.
Blunt Trauma (Bronze)	Acquire your first melee weapon.
Bon Voyage (Silver)	Complete Mission 1 - Smooth Sailing.
Buckshot Ballet (Bronze)	Acquire the shotgun.
Crossing The Rubicon (Silver)	Complete Mission 10 - Faith.
Cutting Edge (Bronze)	Upgrade your stealth kill weapon.
Hard Rain (Silver)	Complete Mission 3 - Echoes.
Hatchet Man (Bronze)	Upgrade your melee weapon.
Improvised Assassin (Bronze)	Acquire your first stealth kill weapon.
Live Together, Die Alone (Silver)	Complete Mission 5 - A Fighting Chance.
Mind Over Mind (Silver)	Complete Mission 11 - Deliverance.
On The Rocks (Silver)	Complete Mission 8 - Devan.
Power To The People (Bronze)	Upgrade the shotgun.
Showdown (Silver)	Complete Mission 9 - Father's Day.
Sign Of Good Faith (Silver)	Complete Mission 6 - Stories of the Dead.
Silent Death (Bronze)	Upgrade the pistol.
Top Of The Line (Bronze)	Upgrade your melee weapon for the third time. Yeah!
Undercover (Silver)	Complete the prologue.
Welcome To The Jungle (Silver)	Complete Mission 2 - One Less Boat.
What A Trip! (Gold)	Complete the game.