Here is the full list of all 23 Super Laser Racer achievements.
Use tractor beam to overtake opponent
Win a race
Complete a lap without taking any damage
Win a Survivor quick race
Win an Eliminator quick race
Unlock all ships
Earn a Special medal
Unlock all tournaments (Hard)
Destroy an opponent with the Cannon
Destroy an opponent with a Laser
Destroy an opponent with a Plasma
Destroy an opponent with a Missile
Destroy an opponent with Mines
Destroy an opponent with a Bomb
Use Shield to protect yourself from a Missile
Destroy multiple enemies in a race
Destroy a Bomb before it explodes
Win a race without using a weapon
Destroy an enemy in your death blast
Special medal for Super tournament (Hard)
Earn all the Special medals on all levels
Destroy mine with an ECM blast
Destroy an opponent with the Super Laser