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