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