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