Here is the full list of all 51 Driver: San Francisco trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Complete Chapter 2
Unlock a Movie Challenge
Shift 1000 times (Story/Online)
Perform a 250m Drift or Jump (Story/Online)
Reach Multiplayer Level 38 (Public)
Keep the Tag for 10s, 50 times in Tag (Public)
Score 10 times in Capture the Flag (Public)
Carry the Torch for 20s, 25 times in Relay Race (Public)
Successfully attack the base 10 times in Blitz (Public)
Reach 25 drop-off locations in Takedown (Public)
Place in the top 3 in Classic Race 10 times (Public)
Place in the top 3 in Sprint GP 10 times (Public)
Spin out 10 Vehicles with Impulse (Public)
Score 1000 gates in Checkpoint/Team Rush (Public)
Reach Multiplayer Level 20 (Public)
Swap or Spawn into 20 Unique Vehicles (Public)
Place in the top 3 in Shift Race 10 times (Public)
Reach Multiplayer Level 5 (Public)
Stay in both trails for 30s in Trailblazer (Public)
Complete Chapter 1
Complete an Activity
Buy your first Vehicle
Complete a Dare
Complete the Prologue
Complete the Shift Tutorial
Collect all Trophies
Complete Chapter 3
Complete Chapter 4
Complete Chapter 5
Complete Chapter 6
Complete Chapter 7
Complete Chapter 8
Complete the Story
Beat the Target Time/Score on any Challenge
Complete the 'Blast from the Past' Challenge
Unlock 6 Movie Challenges
Unlock all 13 Movie Challenges
Complete 25 Activities
Complete 50 Activities
Complete 40 Dares
Complete all 80 Dares
Buy 50 Vehicles
Buy all of the Vehicles from the Garage
Buy your first Garage
Buy all of the Garages in the City
Buy all of the Upgrades from the Garage
Spend 5,000,000 WP
Drive over 1000 miles (~1610 km) (Story/Online)
Complete 30 Freedrive Cop Chases
Complete a Getaway Activity in a Car Transporter
Drive down Lombard Street, no collisions, over 20mph (32 km/h) (Story)