for the car unlock achievements you can enter an arena battle event, destroy some cars, then choose to restart the event and the kills will count towards your total. here are the available arena battle events and the cars in each event:

Episode 1
first event - Testosterone

• Dozer - bulldozer
  
• Shumacher - rally
  
• Buggy - buggy
  
• Shark - racecar
  
• General - army jeep

Episode 2
first event - Autodafe

• Shark - racecar x2
  
• Shumacher - rally x2
  
• Buggy - buggy

Episode 3
eighth(?) event - Battle

• General - army jeep
  
• Shumacher - rally
  
• Buggy - buggy
  
• Dozer - bulldozer
  
• Shark - racecar

for the artist achievement, here are all the skins to unlock per car:

car unlocks through story mission:

• Blue Indigo
  
• Black Devil
  
• Red Skull
  
• Yellow Zombie
  
• Lightning

car unlocks through story mission

• Azure Metallic
  
• Black
  
• Bordeaux
  
• Violet
  
• Ochre

car unlocks through story mission

• Lindworm
  
• Wyvern
  
• No 33
  
• Basilisk
  
• Amphiter

unlock this car by destroying 50 racecars (Shark)

• Calypso
  
• Night
  
• Blood
  
• Tiger
  
• Demon

unlock this car by destroying 10 Army Jeeps (General)

• Khaki
  
• Black
  
• Gold
  
• Glamour
  
• Sand
  
• Urban

unlock this car by destroying 20 rally cars (Schumacher)

• Blue
  
• Lemon
  
• Screwdriver
  
• Pina Colada
  
• Mochito
  
• Black

unlock this car by destroying 40 buggies (Buggy)

• Yes!
  
• Pink Floyd
  
• Lead airship
  
• Deep Purple
  
• Black Sabbath
  
• Yellow Submarine

unlock this car by destroying 5 bulldozers (Dozer)
This car has no skins.