Here is the full list of all 48 LEGO City Undercover achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Achieve LEGO City Hero in any level
Complete Chapter 3 - Go Directly to Jail
Complete the Bucking Bronco game
Complete Chapter 2 - Blast from the Past
Complete Chapter 1 - New Faces and Old Enemies
Complete Chapter 4 - When the Going gets Tough
Complete Chapter 5 - Undercover
Complete Chapter 6 - All in the Family
Complete Chapter 7 - One Small Job for Chan
Complete Chapter 8 - The Rescue
Complete Chapter 9 - Bringing Home the Bacon
Complete Chapter 10 - Back on the Case
Complete Chapter 11 - The Proof of the Pudding is in the Meeting
Complete Chapter 12 - The Con in Construction
Complete Chapter 13 - Secrets
Complete Chapter 14 - Savings and Loans
Complete Chapter 15 - Far Above the Call of Duty
Complete all Free Run Challenges
Complete all Vehicle Races
Complete all Police City Challenges
Complete all Robber City Challenges
Complete all Miner City Challenges
Complete all Astronaut City Challenges
Complete all Farmer City Challenges
Complete all Firefighter City Challenges
Complete all Construction City Challenges
Achieve LEGO City Hero on all levels
Collect all Police Shield pieces in any level
Collect all Police Shield pieces in the game
Achieve 100% Completion
Collect all Red Bricks
Play with all 8 disguise slots customised at the same time
Find and build the 5 hidden Police Shields
Find and destroy the 5 hidden Rex Graffiti Skullptures
Construct all 65 city Super Builds
Build up the brick multiplier to activate the super car
Throw troublemakers into each other 5 times during Gang Fight Challenges
Build all objects in Bright Lights Plaza's LEGO Store
Listen to 20 different conversations whilst Audio Scanning
Use 10 Stunt Ramps in a taxi with a passenger
Drive a lawnmower as Rex Fury
Score 3 baskets in 3 attempts when playing the basketball game
Slide down the hand rail from the top of Fresco's Fusileani Tower
Car surf for 30 seconds
Ride each of the 4 Super Build fairground rides
Jump from a helicopter into a car
Collect 4,000,000,000 LEGO studs
Visit all 10 giant LEGO City stone statues