Get all cars and tracks:
At the main menu, hold R1 + L1 and press Circle, Square, Square, Triangle, X. 

All cars: 
Hit 11 Bonus Stunt items while completing Challenge 8. 

All worlds: 
Find the Hidden Key while completing Challenge 18. 

All items: 
Intentionally hit at least 30 Barrels while completing Challenge 7. 

Upgraded laser: 
Successfully complete Challenge 18 under the very hard difficulty setting. 

Unlimited ammunition: 
Intentionally hit at least 50 Barrels while completing Challenge 18. 

Unlimited health: 
Intentionally hit at least 179 Barrels while completing Challenge 17. 

Unlimited turbo: 
Collect 8 Zappers while completing Challenge 4. 

Timer speed: 
Intentionally hit at least 60 Barrels while completing Challenge 12.