Here is the full list of all 53 Hotshot Racing achievements. It takes around 25-30 hours to unlock all of the achievements on Windows.
Come 1st in 9 online races (any game mode)
Drive or Explode: Cause 3 vehicles to explode within 10 seconds of hitting them.
(Robbers Only) Perform a donut in a race and achieve the highest score.
Set a personal best time on every track. (No mirrored track required.)
In Drive or Explode, crash into another racer causing them to explode.
Drive or Explode: Finish a lap without taking any damage. (Restored health is irrelevant.)
Beat a downloaded ghost time in Time Trial.
(Cops only) Convert a Robber by colliding whilst driving in the wrong direction.
(Cops only) Convert 3 Robbers into Cops in a Cops & Robbers race.
(Cops Only) Convert 2 Robbers within a second of eachother
Finish first in the Boss Level GP on Expert
Come 1st in every GP as any character on Expert.
Purchase all customisation options.
Unlock all customisation options.
Play an Online race.
Play an Online race with a customised vehicle.
Customise every aspect of a vehicle and complete a race with it.
Achieve 1st place as Toshiro in any Grand Prix on Expert.
Achieve 1st place as Mike in any Grand Prix on Expert.
Achieve 1st place as Viktor in any Grand Prix on Expert.
Achieve 1st place as Marcus in any Grand Prix on Expert.
Achieve 1st place as Xing in any Grand Prix on Expert.
Achieve 1st place as Aston in any Grand Prix on Expert.
Achieve 1st place as Alexa in any Grand Prix on Expert.
Achieve 1st place as Keiko in any Grand Prix on Expert.
Complete a race in every vehicle.
Reverse across the finish line and take 1st place in an arcade race.
Drive inside a ghost in Time Trial for 5 seconds.
(Robbers only) Complete a race of Cops & Robbers without being converted into a Cop.
In Drive or Explode, explode before reaching the 1st checkpoint.
Beat a default ghost time in Time Trial.
Build your boost meter to full from empty twice in a race.
Finish a Barrel Barrage race without hitting a single barrel
Finish a Barrel Barrage race on fire
Drive or Explode: Finish a race on fire.
Beat 5 personal bests on any track.
Complete a race on a mirrored track.
Complete a race without colliding with another racer.
Finish a race with 20 track destructibles destroyed.
Cross the finish line on Drive or Explode at 300mph.
Finish an arcade race on every track.
Come 1st in 16 arcade races on different tracks.
Come 1st in 8 arcade races on different tracks.
Come 1st in 4 arcade races on different tracks.
Start the explosion timer 4 times in Drive or Explode.
Come 1st in an Arcade Race after dropping to 8th place from 1st place.
Perform 10 boosts in a race.
Fail a start line boost and take 1st place in arcade mode.
Slipstream behind a player for 5 seconds.
Come 1st in an arcade race.
Exit a Drift with a Boost.
Build a full boost bar segment from one drift.
Come 1st and beat 2nd place by 1 second.