There are 41 Trophies that can be collected.

Bronze

Invasion
Clear Mission 1.

Diversion
Clear Mission 2.

Central Battery
Clear Mission 3.

Distress Call
Clear Mission 4.

Possession
Clear Mission 5.

Corruption
Clear Mission 6.

Biot
Clear Mission 7.

Hot Pursuit
Clear Mission 8.

Ultimate Weapon
Clear Mission 9.

Return to Oa
Clear Mission 10.

Synergy
Clear a mission in Co-op.

Just Getting Started
Perform a 20 hit combo.

Master Blaster
Defeat 10 enemies with Ring Blaster.

Blunt Justice
Defeat 10 enemies with War Hammer.

Demolitionist
Defeat 10 enemies with Hover Mines.

Favorite Pastime
Defeat 10 enemies with Baseball Bat.

All in the Wrist
Defeat 10 enemies with Blade Whip.

Locked and Loaded
Defeat 10 enemies with Gatling Gun.

Lights Out
Defeat 10 enemies with Piston Blitz.

Fan Favorite
Defeat 10 enemies with Rocket Punch.

Targets Acquired
Defeat 20 enemies with Missile Pack.

Big Beat Down
Defeat 20 enemies with Mech Suit.

Around the World
Defeat 20 enemies with Mace Storm.

Hal Knows Jets
Defeat 20 enemies with Jet Fighter.

Beware My Power!
Use Ring Surge 10 times.

What Goes Up…
Launch 20 enemies.

Get Dizzy Yall
Make Green Lantern dizzy 10 times.

Silver

Emerald Warrior
Complete the game on Poozer of Enforcer difficulty.

On a Roll
Perform a 50 hit combo.

Rank Up
Gain experience level 5.

There is Hope
Collect all 5 Blue Meteorites.

Mogo is Proud
Collect all 9 Green Meteorites.

Might Makes Right
Purchase all Attack upgrades.

Full Burn
Purchase all Ring Surge upgrades.

Complete Control
Purchase all Ring Power upgrades.

Willpower
Purchase all Construct upgrades.

Gold

Emerald Knight
Clear all missions on Emerald Knight difficulty.

Shut Your Mouth
Perform a 99 hit combo.

Not a Poozer
Gain experience level 10.

Big Spender
Purchase all upgrades.

Platinum

Fear This!
Collect all trophies.

http://www.ps3trophies.com/forums/trophy-news/62124-green-lantern-rise-manhunters-trophy-list.html