Here is the full list of all 45 Generator Rex: Agent of Providence trophies - there are 30 bronze, 11 silver, 3 gold and 1 platinum.
Unlock All Generator Rex Trophies
Successfully Fly Through The Circular Debris While Sky Diving
Complete The Tutorial In Mexico
Defeat The Multi-Head EVO
Defeat The EVO Death Bunny
Solve The Puzzle In The Temple
Encounter Circe
Recover the Funchucks in Hong Kong
Save Doctor Holiday
Defeat Van Kleiss In Providence
Acquire The Bad Axes
Defeat Biowulf
Cure Aquania
Acquire The Blast Caster
Defeat Breach
Complete The Rex Ride Sequence
Defeat Giant Van Kleiss
Finish The Campaign
Gather All Computer Info From Dr. Rylander's Lab
Get The First Item Of Rex's Past
Collect All Items Of Rex's Past
Collect The 1st Sample For Doctor Holiday
Collect All The Samples Of Any 2 EVOs
Collect All The Samples For Doctor Holiday
Purchase An Upgrade
Purchase All Upgrades
Open 30 Supply Boxes
Defeat 200 Enemies
Defeat 100 Enemies With The Smack Hands
Defeat 100 Enemies With The BFS
Defeat 100 Enemies With The Slam Cannon
Defeat 100 Enemies With The Punk Busters
Defeat 100 Enemies With Omega Builds
Get A 20 Hit Combo
Get A 60 Hit Combo
Beat One Agent Six Time Challenge Level
Beat Any One Agent Six Time Challenge In Under 10 Mins.
Beat All Agent Six Time Challenges
Knock 20 EVOs Out Of The World
Collect All The Nanites And Do Not Get Hurt In Sky Diving
Kill All EVOs And Take No Damage In Rex Ride
Indirectly Defeat 30 EVOs
Successfully Wiggle Free Of 20 Spider Webs Without Taking Damage
Beat Quarry In 2.5 Mins. Or Less
Defeat Van Kleiss In Abysus Castle Without Taking Any Damage