Here is the full list of all 16 Concept Destruction achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Win the Championship
Survive over 3 minutes in Survival mode
Drive over 5 minutes in Tourism mode
Destroy car "TIFA X/2" using car "ZIP JX"
Get out of the driving area in School
Hit the hidden ball in "The Stadium"
Destroy a rival car in Tourism mode
Pass all school lessons
Drive through one of the goal posts in "The Stadium"
Get to the paint zone in "The Rooftop"
Jump and stay in air for more than 3 seconds
Pick up 5 batteries from other cars (it doesn't need to happen in a single event)
Get out of the arena in "The Bulls"
Destroy 3 rival cars in a single event
Drive on the roof in "The Plaza"
Destroy a rival car