Here is the full list of all 44 Generator Rex: Agent of Providence achievements worth 1,000 gamerscore.
Collected All The Samples For Doctor Holiday
Defeated 100 Enemies With The Punk Busters
Beat All Agent Six Time Challenges
Indirectly Defeated 30 EVOs
Knocked 20 EVOs Out Of The World
Beat Any One Agent Six Time Challenge In Under 10 Mins.
Killed All EVOs And Take No Damage In Rex Ride
Gathered All Computer Info From Dr. Rylander's Lab
Beat One Agent Six Time Challenge Level
All Upgrades Purchased
Collected All The Nanites And Did Not Get Hurt In Sky Diving
Finished The Campaign
Defeated Giant Van Kleiss
Defeated Van Kleiss In Abysus Castle Without Taking Any Damage
Defeated 100 Enemies With Omega Builds
Collected All Items Of Rex's Past
Defeated Breach
Opened 30 Supply Boxes
Cured Aquania
Acquired The Blast Caster
Defeated 100 Enemies With The Slam Cannon
Defeated Biowulf
Defeated Van Kleiss In Providence
Saved Doctor Holiday
Successfully Wiggled Free Of 20 Spider Webs Without Taking Damage
Acquired The Bad Axes
Defeated 100 Enemies With The Smack Hands
Beat Quarry In 2.5 Mins. Or Less
Collected All The Samples Of Any 2 EVOs
Recovered The Funchucks in Hong Kong
Defeated 200 Enemies
Completed The Rex Ride Sequence
Encountered Circe
Defeated The EVO Death Bunny
Solved The Puzzle In The Temple
Defeated 100 Enemies With The BFS
Got A 60 Hit Combo
Collected The 1st Sample For Doctor Holiday
First Upgrade Purchased
Defeated The Multi-Head EVO
Got The First Item Of Rex's Past
Completed The Tutorial In Mexico
Got A 20 Hit Combo
Successfully Flew Through The Circular Debris While Sky Diving