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