Here is the full list of all 42 Need for Speed Heat achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Change the text on the License Plate
Complete Chapter 1
Complete 5 events online with other players
Repair critical damage at a Gas Station at night
Complete your first Daily Challenge
Reach REP Level 2
Pick your first ride
Complete Chapter 2
Complete Chapter 3
Complete Chapter 4
Take down 100 Cop Vehicles
Hit 240 mph using any car
Get a 3 Star Rating on all the Activities in the game
Beat your first Crew Time Trial
Smash your way through all the Billboards
Win a race with a car at 399 Performance Rating
Get all Collectibles and 3 stars on all Activities
Go from last to first place during the final lap of a race and win
Complete the Drift driving story
Complete the Off-road driving story
Complete the Race driving story
Customize a vehicle with a wrap
Complete all Drift Zones
Win a race with parts equipped in both auxiliary part slots
Win a race with all vehicle effects slots equipped
Escape 100 Cop Chases
Complete 25 events online with other players
Collect all the Flamingos
Collect all Street Art
Win a High Heat 5 race and return to garage safely
Complete all Long Jumps
Reach max Crew Level with your Crew
Win a race with handling parts for maximum drift equipped
Win a race with handling parts for maximum off-road traction equipped
Win a race with handling parts for maximum road traction equipped
Win a race with handling parts for maximum race equipped
Reach REP Level 50
Earn and bank 1 000 000 REP during one night
Complete all Speed Traps
Win a race in a vehicle with an engine swap
Win the Discovery Event
Win a race in a vehicle with tuned exhaust sound