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