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