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