Complete the following tasks to unlock Vita trophy rewards.

Trophy	How to unlock
...and Practice (Bronze)	Build a Workshop.
A Little Bit Alien (Bronze)	Modify a soldier.
Ain't No Cavalry Comin' (Silver)	Have a soldier survive every mission in a full game.
All Employees Must Wash Hands... (Bronze)	In a single game, complete every Autopsy.
All Together Now (Bronze)	Get satellite coverage over every country on one continent.
And So It Begins... (Bronze)	Complete the tutorial mission.
Apotheosis Denied (Silver)	Deal with the newest global threat.
Beyond the Veil (Bronze)	Find a soldier with the Gift.
Drums in the Deep (Bronze)	Gain access to the lowest level in your base.
Earth First (Silver)	Beat the game on Classic difficulty.
Edison (Bronze)	In a single game, complete every Research Project.
Elite Defense (Silver)	Beat a new special mission without losing any assets.
Enemy Within (Silver)	Get a Soldier to have 5 modifications.
Eye in the Sky (Bronze)	Launch a Satellite.
Flight of the Valkyries (Bronze)	Win a mission with an all-female squad.
Guardian of Earth (Silver)	Designate a highly decorated soldier as the Volunteer.
Happy to Oblige (Bronze)	Fulfill a Council request.
Humanity's Savior (Bronze)	Beat the game on any difficulty.
Hunter/Killer (Bronze)	In a single game, shoot down one of each alien craft.
Lone Wolf (Silver)	Clear a UFO crash site with one soldier on Classic or Impossible difficulty.
Mental Minefield (Bronze)	Kill an enemy as it is psionically attacking you.
No Looking Back (Gold)	Beat the game in Ironman mode on Classic or Impossible difficulty.
Off My Planet (Bronze)	Recover the Hyperwave Beacon.
On the Shoulders of Giants (Bronze)	Build the Gollop Chamber.
Our Finest Hour (Gold)	Beat the game on Impossible difficulty.
Pain in the Neck (Bronze)	Cause an enemy to suicide.
Prisoner of War (Bronze)	Capture a live alien.
Rise of the Machines (Bronze)	Field a squad consisting entirely of augmented soldiers and SHIVs (min. 4) and win the mission.
Skunkworks (Bronze)	In a single game, complete every Foundry project.
Someone Your Own Size (Bronze)	Kill a Muton Berserker in melee combat.
Steel Martyr (Silver)	Deploy three tactical subsystems on a single soldier.
Tables Turned (Bronze)	Shoot down a UFO.
The Gatekeeper (Bronze)	Stun an Outsider.
The Hardest Road (Silver)	Advance one of your soldiers to Colonel rank.
The Volunteer (Bronze)	Make contact with the Ethereal hive mind.
Theory... (Bronze)	Build a Laboratory.
They Shall Not Pass (Bronze)	Eliminate all alien waves.
Tingling Sensation (Bronze)	Kill an unseen enemy detected by a specially modified soldier.
We Happy Few (Bronze)	Complete a mission without losing a soldier.
Welcoming Committee (Bronze)	Kill 150 aliens.
Wet Work (Silver)	Complete a Very Difficult abduction mission in five turns or less on Classic or Impossible difficulty.
Where in the World (Silver)	Make certain of the new threat's location.
Who Needs Limbs? (Bronze)	Augment a soldier.
Worth Every Penny (Bronze)	Acquire 1000 credits in one month.
X Marks the Spot (Bronze)	Uncover the alien base's location.
Xavier (Bronze)	Mind Control an Ethereal.
You Win (Platinum)	You Win, Everything.
Zom-B-Gone (Bronze)	Eradicate the infestation.