Here is the full list of all 43 Need for Speed Heat trophies - there are 31 bronze, 8 silver, 3 gold and 1 platinum.
Collect all trophies
Escape 100 Cop Chases
Reach max Crew Level with your Crew
Win the Discovery Event
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
Smash your way through all the Billboards
Complete all Long Jumps
Collect all the Flamingos
Collect all Street Art
Complete all Speed Traps
Win a race with a car at 400+ Performance Rating
Complete 25 events online with other players
Reach REP Level 50
Earn and bank 1 000 000 REP during one night
Complete the Race driving story
Win a High Heat 5 race and return to garage safely
Take down 100 Cop Vehicles
Complete the Off-road driving story
Complete 5 events online with other players
Win a race with handling parts for maximum off-road traction equipped
Hit 240 mph using any car
Complete Chapter 4
Complete the Drift driving story
Win a race in a vehicle with an engine swap
Complete Chapter 3
Win a race with all vehicle effects slots equipped
Win a race with handling parts for maximum race equipped
Win a race with handling parts for maximum road traction equipped
Win a race with handling parts for maximum drift equipped
Complete Chapter 2
Win a race with parts equipped in both auxiliary part slots
Beat your first Crew Time Trial
Complete Chapter 1
Change the text on the License Plate
Customize a vehicle with a wrap
Go from last to first place during the final lap of a race and win
Repair critical damage at a Gas Station at night
Complete your first Daily Challenge
Reach REP Level 2
Win a race in a vehicle with tuned exhaust sound
Pick your first ride