There are 37 Trophies that can be collected.

Bronze

Recruit
Survive 60 seconds in a public multiplayer match without being killed.

Power Surge
Use an active ability 5 times in a public multiplayer match.

I know what I'm doing!
Change into vehicle form before reaching the change form tutorial in Chapter I.

Boot Stomper
Kill 3 Enemies with Bumblebee's Kick Ability in Chapter I.

Seek and Destroy
Kill 25 Enemies using Grenade Blossom in Chapter II.

Rule With an Iron Fist
Kill 20 enemies with Ironhide's Melee attack in Chapter II.

Body Count
While holding out for Reynolds to send backup in Chapter III, 30 Decepticons are killed.

Good Driver Discount
Avoid taking any damage from Starscream's proximity mines in Chapter III.

Serrated
Kill 10 Autobots with Laserbeak's ram ability in Chapter IV.

Stunning!
Stun 10 Autobots with Soundwave's stun ability in Chapter IV.

Homewrecker
Wipe out all secret base ground defenders within 60 seconds in Chapter V.

Furious Flyer
Fly through the canyons after Air Raid in 120 seconds in Chapter V.

Surprise Package
In the air battle, activate Starscream's Guided Missile ability 5 times without dying in Chapter V.

Autobots are Weak!
Defeat all 3 waves in Megatron's Lair without dying on Hard Difficulty in Chapter VI.

Overlord
Drain 5000 health from enemies in Chapter VI.

Fleet of Foot
When one Driller arm is attacking, avoid all attacks in Chapter VII.

Counting Coup
Use only melee attacks on Shockwave's power core to make him retreat to his cryo platform.

Primed for Combat
Activate Optimus' Shoulder Rocket ability 5 times without dying in Chapter VII.

Silver

Road Kill
Destroy 30 enemies while in vehicle form in Campaign.

Grenade Expert
Eliminate 20 opponents with the Flak Grenade in Campaign.

Chapter I
Complete Chapter I on any difficulty.

Top Score: Bumblebee
Complete Chapter I with a score of 1000000 or more.

Chapter II
Complete Chapter II on any difficulty.

Top Score: Ironhide
Complete Chapter II with a score of 1000000 or more.

Chapter III
Complete Chapter III on any difficulty.

Top Score: Mirage
Complete Chapter III with a score of 800000 or more.

Chapter IV
Complete Chapter IV on any difficulty.

Top Score: Soundwave
Complete Chapter IV with a score of 1000000 or more.

Chapter V
Complete Chapter V on any difficulty.

Chapter VI
Complete Chapter VI on any difficulty.

Top Score: Megatron
Complete Chapter VI with a score of 2000000 or more.

Chapter VII
Complete Chapter VII on any difficulty.

Gold

Prime
Complete the Campaign.

Completionist
Destroy all hidden TRANSFORMERS symbols in Campaign.

The Champion
Reach level 20 in any single class in Multiplayer.

Platinum

AllSpark
Unlock All Trophies.

1 Secret

Bronze

Sacrifice
Be the first one eliminated in a public multiplayer match.

http://www.ps3trophies.org/game/transformers-dark-of-the-moon/trophies/