Here is the full list of all 63 Battle Riders achievements.
Win 20 events with the Vector
Wreck 100 cars with Missiles
Wreck 100 cars with the EMP
Wreck 50 cars with Missiles
Win 20 events with the Tempest
Win all Career events
Win 20 Survival events
Win 40 Battle Race events
Wreck 50 cars with the EMP
Win 10 Time Trial events
Wreck 10 cars with Missiles
Win 20 events with the Meteor
Wreck 100 cars with the Machinegun
Unlock all Metropolis tracks
Win 10 Duel events
Wreck 10 cars with the EMP
Wreck 100 cars with Mines
Win 20 events with the Iridium
Win 10 Clean Race events
Win 10 Elimination events
Win all Tier 2 events
Repair your car 100 times
Win 20 events with the Sabre
Win 10 Survival events
Unlock all Canyon tracks
Wreck 50 cars with the Machinegun
Win 5 Time Trial events
Win 5 Duel events
Win 20 Battle Race events
Wreck 100 cars
Unlock all City Limits tracks
Wreck 50 cars with Mines
Win 20 events with the Blaze
Win 5 Clean Race events
Repair your car 50 times
Win 5 Elimination events
Win all Tier 1 events
Win 20 events with the Raptor
Wreck 10 cars with Mines
Wreck 30 cars
Win a Duel event
Wreck 10 cars with the Machinegun
Win a Clean Race event
Repair your car 10 times
Win a Time Trial event
Win an Elimination event
Win a Survival event
Win a Battle Race event
Wreck a car
Wreck 500 cars
Wreck 1000 cars
Wreck 10 cars with the Raygun
Wreck 50 cars with the Raygun
Wreck 100 cars with the Raygun
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