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