Here is the full list of all 51 Singularity trophies - there are 34 bronze, 15 silver, 1 gold and 1 platinum.
You collected all the trophies for Singularity
Killed 10 enemies by aging a Revert and having it explode near them in single player campaign
Used the TMD to revert 10 Chalkboards in single player campaign
You chose to live and rule the world alone
You chose to live and join Demichev
You sacrificed yourself to stop Demichev
Completed Singularity on Hard Mode
Completed Singularity
Used the TMD to find 15 Chrono-Notes in single player campaign
Kill 5 enemies by grabbing rockets and launching them back in single player campaign
Found the wheel. Will they ever explain this?
20 Centurion kills in single player campaign
Kill 10 enemies inside a Deadlock in single player campaign
Completed the E99 Processing Complex Mission
Purchased 10 different Hero Upgrades in single player campaign
20 Spikeshot kills in single player campaign
Kill 10 enemies with Propane Tanks or Cryo Tanks in single player campaign
20 Dethex Launcher kills in single player campaign
Turn 15 soldiers into Reverts in single player campaign
Grab 5 Shields from enemies in single player campaign
Purchased 5 different TMD Equipment items in single player campaign
15 Autocannon kills without reloading in single player campaign
Completed the Central Docks Mission
Fully Upgraded 1 Weapon in single player campaign
Discovered the strange E99 specimen and what it morphs people into
Completed the Rail Line Mission
Age 15 soldiers to Dust in single player campaign
30 Volk S4 kills in single player campaign
Kill 20 enemies with Impulse in single player campaign
Completed the Research Facility Mission
15 Seeker kills in single player campaign
40 AR9 Valkyrie kills in single player campaign
Completed the Workers' District Mission
25 Kasimov SNV-E99 slo-mo kills in single player campaign
Play 100 public matches of Extermination
Renew 25 beacons in Extermination (public match)
Win 25 public matches of Extermination
Win 25 public matches of Creatures Vs. Soldiers
Play 5 public matches of Extermination
Possess 15 soldiers with tick leap attack (public match)
Kill 15 soldiers with each creature (public match)
Possess a soldier, then shoot another soldier in the face (public match)
Kill 15 soldiers from behind with the Zek (public match)
Kill 15 creatures with the Lurker's reflective shield damage from a melee hit (public match)
Kill 15 soldiers with a Zek barrel (public match)
Travel 585 meters using the Blitzer's Teleport power (public match)
Get highest number of kills in a public match
Kill 25 soldiers with the Revert puke (public match)
Kill 25 creatures with the Bruiser's Impulse Power (public match)
Kill 25 soldiers with the Radion's lob attack (public match)
Use the Healer's power to restore 25 soldiers to full health (public match)