Here is the full list of all 56 Burnout Paradise Remastered achievements.
Repair your first wrecked car
Set a Time Road Rule on Watt St
Set a Showtime Road Rule on East Crawford Drive
Win a Race
Collect 5 Billboards
Collect 25 Smashes
Get 10 Takedowns in Road Rage without Wrecking
Repair your car at critical damage in a Road Rage event
Perform a 360 Flatspin in any car
Get your C Class License
Successfully land 5 Superjumps
Win a Marked Man without being taken down
Get a x10 multiplier in Showtime
Get your B Class License
Power Park with a 100% rating
Land a 2 barrel roll jump
Get a x20 Boost Chain
Find all Events
Set a Showtime Road Rule on every road
Get your D class license
Get a Takedown Rampage
Get your A Class License
Score over 1,000,000 in Stunt Run
Win 25 Burning Routes
Get 500 Takedowns (either online or offline)
Win your Burnout Driving License
Win all Burning Routes
Find all Carparks
Collect all Billboards
Collect all Smashes
Successfully land all Superjumps
Set a Time Road Rule on every road
Find all Drive Thrus and Car Parks
Win your Burnout Elite License
Get your Elite License, win every event, find all discoverables and beat every Road Rule
Complete an online race
Win your first 8 player online race
Win 10 online Races
Complete 20 online Events
Make 50 online Rivals
Make your first online Rival
Complete 1 online Challenge (Timed & Bike challenges do not count)
Complete 25 online Challenges (Timed & Bike challenges do not count)
Complete 250 online Challenges (Timed & Bike challenges do not count)
Complete 2 whole sections of online Challenges (Timed & Bike challenges are not required to be finished)
In an 8 player online Freeburn lead 6 of the Today's Best Scores (6/11 for Cars) (6/6 for Bikes)
Complete a Party game where every player scores in every round
Complete a party game of 8 rounds with 8 players
Awarded for being on the winning Cops team in a Cops and Robbers game
Awarded for being on the winning Robbers team in a Cops and Robbers game
Awarded for delivering the Gold to your team base in a Cops and Robbers game
Collect 20 Island Smashes
Collect 15 Island Billboards
Find all 15 Island events
Land the Mega Jump from the Crash TV Ski Jump with at least 4.5 seconds of Air Time
Awarded when you complete all 10 Island Freeburn Challenges (2 - 8 players)