Here is the full list of all 48 XCOM: Enemy Unknown Plus trophies - there are 34 bronze, 11 silver, 2 gold and 1 platinum.
Beat the game on any difficulty.
Designate a highly decorated soldier as the Volunteer.
Make contact with the Ethereal hive mind.
In a single game, complete every Research Project.
In a single game, shoot down one of each alien craft.
Field a squad consisting entirely of augmented soldiers and SHIVs (min. 4) and win the mission.
Build the Gollop Chamber.
Gain access to the lowest level in your base.
Find a soldier with the Gift.
In a single game, complete every Foundry project.
In a single game, complete every Autopsy.
Eliminate all alien waves.
Recover the Hyperwave Beacon.
Deal with the newest global threat.
Make certain of the new threat's location.
Get a Soldier to have 5 modifications.
Build a Workshop.
Build a Laboratory.
Win a mission with an all-female squad.
Beat a new special mission without losing any assets.
Uncover the alien base's location.
Stun an Outsider.
Deploy three tactical subsystems on a single soldier.
Advance one of your soldiers to Colonel rank.
Kill a Muton Berserker in melee combat.
Augment a soldier.
Eradicate the infestation.
Acquire 1000 credits in one month.
Get satellite coverage over every country on one continent.
Kill 150 aliens.
Cause an enemy to suicide.
Fulfill a Council request.
Modify a soldier.
Capture a live alien.
Shoot down a UFO.
Launch a Satellite.
Complete a mission without losing a soldier.
Complete the tutorial mission.
You Win, Everything.
Kill an enemy as it is psionically attacking you.
Kill an unseen enemy detected by a specially modified soldier.
Beat the game in Ironman mode on Classic or Impossible difficulty.
Mind Control an Ethereal.
Beat the game on Classic difficulty.
Beat the game on Impossible difficulty.
Clear a UFO crash site with one soldier on Classic or Impossible difficulty.
Have a soldier survive every mission in a full game.
Complete a Very Difficult abduction mission in five turns or less on Classic or Impossible difficulty.