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