There are 51 Trophies that can be collected.

BRONZE

Humanity's Savior
Beat the game on any difficulty.

Bada Boom
Kill 50 aliens with explosive weapons.

Welcoming Committee
Kill 150 aliens.

As A Scalpel
Earn the "Excellent" rating in every performance category on a terror mission.

Edison
In a single game, complete every Research Project.

All Employees Must Wash Hands…
In a single game, complete every Autopsy.

Eye in the Sky
Launch a Satellite.

All Together Now
Get satellite coverage over every country on one continent.

Hunter/Killer
In a single game, shoot down one of each alien craft.

Man No More
Build a suit of powered armor.

We Happy Few
Complete a mission without losing a soldier.

Worth Every Penny
Acquire 1000 credits in one month.

Oppenheimer
Staff the Research Labs with 80 scientists.

One Gun at a Time
Staff the Engineering Department with 80 engineers.

Skunkworks
In a single game, complete every Foundry project.

You Have 5 Seconds to Comply
Build a S.H.I.V

Theory…
Build a Laboratory.

…and Practice
Build a Workshop.

What Wonders Await
Complete a Research Project.

Up and Running
Build a base facility.

Combat Ready
Build an item.

Drums in the Deep
Gain access to the lowest level in your base.

Happy to Oblige
Fulfill a Council request.

Tables Turned
Shoot down a UFO.

And So It Begins…
Complete the tutorial mission.

SILVER

Earth First
Beat the game on Classic difficulty.

Lone Wolf
Clear a UFO crash site with one soldier on Classic or Impossible difficulty.

Pale Horse
Kill 500 aliens.

Shooting Stars
Shoot down 40 UFOs.

Ain't No Cavalry Comin'
Have a soldier survive every mission in a full game.

The Hardest Road
Advance one of your soldiers to Colonel rank.

Wet Work
Complete a Very Difficult abduction mission in five turns or less on Classic or Impossible difficulty.

A Continental Fellow
Win the game from each of the 5 starting locations.

GOLD

No Looking Back
Beat the game in Ironman mode on Classic or Impossible difficulty.

Our Finest Hour
Beat the game on Impossible difficulty.

PLATINUM

You Win
Gain all trophies.

15 SECRET

http://www.ps3trophies.org/game/xcom-enemy-unknown/trophies/