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