There are 51 Trophies that can be earned in this title.

Bronze

Pistol Whipped
20 Centurion kills in single player campaign

A Salt and Battery
40 AR9 Valkyrie kills in single player campaign

Double Barrel
30 Volk S4 kills in single player campaign

The Slower the Better
25 Kasimov SNV-E99 slo-mo kills in single player campaign

You're a Hit
20 Spikeshot kills in single player campaign

Roller Derby
20 Dethex Launcher kills in single player campaign

Drive By
15 Seeker kills in single player campaign

Return to Sender
Kill 5 enemies by grabbing rockets and launching them back in single player campaign

Put the Dead in Deadlock
Kill 10 enemies inside a Deadlock in single player campaign

Up Close and Personal
Kill 20 enemies with Implus in single player campaign

Fire and Ice
Kill 10 enemies with Propane Tanks or Cyro Tanks in single player campaign

Time Bandit
Grab 5 Shields from enemies in single player campaign

Ashes to Ashes
Age 15 soldiers to Dust in single player campaign

Night of the Living Revert
Turn 15 soldiers in Reverts in single player campaign

Fully Armed
Fully Upgraded 1 Weapon in single player campaign

E99 Tech Geek
Purchased 10 different Hero Upgrades in single player campaign

Time's on My Side
Purchased 5 different TMD Equipment items in single player campaign

Pen Pal
Used the TMD to find 15 Chronic-Notes in single player campaign

Stay After Class
Used the TMD to revert 10 Chalkboards in single player campaign

That Wheel?
Found the wheel. Will they ever explain this?

Mother My Brain Hurts
Discovered the strange E99 specimen and what it morphs people into

Extermination Expert
Play 5 public matches of Extermination

CvS Master
Win 25 public matches of Creatures vs. Soldiers

Creature Hater
Renew 25 beacons in Extermination (public match)

Creature Lover
Kill 15 soldiers with each creature (public match)

Fastball
Kill 15 soldiers with a Zek barrel (public match)

Zekky Style
Kill 15 soldiers from behind with the Zek (public match)

Hot Lunch Special
Kill 25 soldiers with the Revery puke (public match)

Bombs over Katorga
Kill 25 soldiers with the Radion's Iob attack (public match)

Talk to the Hand
Kill 25 creatures with the Bruiser's Impulse Power (public match)

Dr. Hand
Use the Healer's power to restore 25 soldiers to full health (public match)

Don't Touch Me!
Kill 15 creatures with the Lurker's reflective shield damage from a melee hit (public match)

Blitzkrieg
Travel 585 meters using the Blitzer's Teleport power (public match)

Killer
Get highest number of kills in a public match

Silver

No Time to Bleed
15 Autocannon kills without reloading in single player campaign

Revert Bomber
Killed 10 enemies by again a Revert and having it explode near them in single player campaign

Extermination Addict
Play 100 public matches of Extermination

Extermination Master
Win 25 public matches of Extermination

In Yo Face
Possess 15 soldiers with tick leap attack (public match)

The VP Treatment
Possess a soldier, then shoot another soldier in the face (public match)

Gold

Time Master
Completed Singularity on Hard Mode

Platinum

Platinum Singularity
You collected all the trophies for Singularity

9 Secret

http://www.ps3trophies.org/game/singularity/trophies/