Here is the full list of all 44 Generator Rex: Agent of Providence achievements worth 1,000 gamerscore.
Defeated Breach
Defeated 100 Enemies With The Slam Cannon
Cured Aquania
Opened 30 Supply Boxes
Acquired The Blast Caster
Defeated Biowulf
Defeated Van Kleiss In Providence
Defeated 100 Enemies With The Smack Hands
Saved Doctor Holiday
Acquired The Bad Axes
Beat Quarry In 2.5 Mins. Or Less
Defeated 200 Enemies
Collected All The Samples Of Any 2 EVOs
Recovered The Funchucks in Hong Kong
Completed The Rex Ride Sequence
Encountered Circe
Defeated The EVO Death Bunny
Solved The Puzzle In The Temple
Successfully Wiggled Free Of 20 Spider Webs Without Taking Damage
Defeated 100 Enemies With The BFS
Got A 60 Hit Combo
Collected The 1st Sample For Doctor Holiday
Got A 20 Hit Combo
First Upgrade Purchased
Got The First Item Of Rex's Past
Defeated The Multi-Head EVO
Completed The Tutorial In Mexico
Successfully Flew Through The Circular Debris While Sky Diving
Defeat Giant Van Kleiss
Finish The Campaign
Gather All Computer Info From Dr. Rylander's Lab
Collect All Items Of Rex's Past
Collect All The Samples For Doctor Holiday
Purchase All Upgrades
Defeat 100 Enemies With The Punk Busters
Defeat 100 Enemies With Omega Builds
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
Defeat Van Kleiss In Abysus Castle Without Taking Any Damage