Here is the full list of all 63 Battle Riders achievements.
Win a Battle Race event
Win all Tier 1 events
Win all Tier 2 events
Win all Career events
Win a Duel event
Win 5 Duel events
Win 10 Duel events
Win 20 Battle Race events
Win 40 Battle Race events
Win a Survival event
Win 10 Survival events
Win 20 Survival events
Win an Elimination event
Win 5 Elimination events
Win 10 Elimination events
Win a Clean Race event
Win 5 Clean Race events
Win 10 Clean Race events
Win a Time Trial event
Win 5 Time Trial events
Win 10 Time Trial events
Win 20 events with the Raptor
Win 20 events with the Blaze
Win 20 events with the Sabre
Win 20 events with the Iridium
Win 20 events with the Meteor
Win 20 events with the Tempest
Win 20 events with the Vector
Wreck a car
Wreck 30 cars
Wreck 100 cars
Wreck 500 cars
Wreck 1000 cars
Wreck 10 cars with the Machinegun
Wreck 50 cars with the Machinegun
Wreck 100 cars with the Machinegun
Wreck 10 cars with Missiles
Wreck 50 cars with Missiles
Wreck 100 cars with Missiles
Wreck 10 cars with Mines
Wreck 50 cars with Mines
Wreck 100 cars with Mines
Wreck 10 cars with the EMP
Wreck 50 cars with the EMP
Wreck 100 cars with the EMP
Wreck 10 cars with the Raygun
Wreck 50 cars with the Raygun
Wreck 100 cars with the Raygun
Repair your car 10 times
Repair your car 50 times
Repair your car 100 times
Unlock all City Limits tracks
Unlock all Canyon tracks
Unlock all Metropolis tracks
Achieve under 1:01 in a Time Attack challenge
Achieve under 1:01 in 9 different Time Attack challenges
Achieve under 1:01 in 18 different Time Attack challenges
Reach 330 in a Minefield challenge
Reach 330 in 9 different Minefield challenges
Reach 330 in 18 different Minefield challenges
Hit at least 120 barrels in a Barrels challenge
Hit at least 120 barrels in 9 different Barrels challenges
Hit at least 120 barrels in 18 different Barrels challenges