Here is the full list of all 33 Rebel Cops achievements.
Complete all the extra jobs in the game
Buy everything in the store
Max out your Street Cred
Achieve the minimum Street Cred
Give 50% of your income to the citizens
Don't give the citizens a single penny
Complete all missions in one play-through with no more than three cops
Arrest 101 criminals
Expand your cops' inventory
Wound 20 criminals in the leg
Complete any mission with one cop
Raise one of your cops to level 10
Use "Shock and Awe" three times in a single play-through
Raise a cop two levels in a single mission
Fulfill an extra job to help catch Warren Nash
Complete the game on Normal Mode
Complete the game on Relaxed Mode
Prevent a bank robbery with all your cops intact
Complete the "Railway Station" mission
Agree to help the owner of the photo studio for free
Drive the criminals from the photo studio
Complete the "Estate" mission
Complete the "Big Rift" mission
Complete the "Bookstore" mission
Complete the "Construction Site" mission
Complete the "Airport" mission
Protect the photo studio from a criminal assault
Complete the "Mine" mission
Complete the “DDM” mission
Complete the "Colors of Life Commune"
Complete the "Casino" mission
Complete the “Mansion” mission
Complete the game on Hard Mode