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