Here is the full list of all 41 Dangerous Driving trophies - there are 22 bronze, 15 silver, 3 gold and 1 platinum.
Win a Takedown Race after being in last place on the last lap
Gold Medal a Road Rage without crashing
Complete all Sedan Class events
Win a GP
Drive 5 miles in a Survival
Empty a full Boost Bar in one go in Survival
Gold Medal a Survival
Unlock Prototype Sedan
Get a Gold Medal in Pursuit
Win a Pursuit
Drive 100 miles in any car
Take down your opponent 5 times in a single Face Off
Get a Shakedown Gold Medal
Win a Shakedown without crashing
Get a 10x Heatwave
Get a 3x Heatwave
Win a Face Off
Win a Road Rage
Win a Takedown Race
Get a Double Takedown
Get a Takedown Hot Streak
Platinum Trophy
Win every round of a GP
Complete all SUV Class events
Complete all Coupe Class events
Complete all Supercar Class events
Complete all Hypercar Class events
Gold medal all Pursuits
Gold medal all Takedown Races
Gold medal all Road Rages
Gold medal all Shakedowns
Gold medal all Face Offs
Gold medal all Survivals
Unlock Prototype SUV
Unlock Prototype Coupe
Unlock Prototype Supercar
Unlock Prototype Hypercar
Unlock Prototype Formula DD
Drive 1000 miles in any car
Drive 50 miles in every car
Drive 100 miles in every car