Here is the full list of all 30 Carmageddon: Reincarnation achievements.
Complete the They Don't Like It Up 'Em Challenge
Kill 100 targeted Peds in Ped Chase
Wreck 100 Opponents in Car Crusher
Finish one Classic Carma Event in all three ways
Hit 100 Checkpoints in Checkpoint Stampede
Finish a Classic Carma Event by Killing all the Peds
Complete the Bulging Purse Challenge
Complete the Hotwiring Hotstuff Challenge
Complete the Up Your Carma Challenge
Complete the Split Personality Challenge
Buy all Parts in the Parts Shop for one Car
Unlock Chapter 10 in the Career
Finish a Classic Carma Event by Completing all the Laps
Achieve a Suck My Parts or Collateral Damage Bonus
Get a x10 Ped Kill Combo
Buy your first Part from the Parts Shop
Unlock Chapter 2 in the Career
Complete 50 different Career Events on any Difficulty
Finish a Classic Carma Event by Wrecking all the Opponents
Wreck your first Opponent
Own Carmageddon Max Pack, Carmageddon 2: Carpocalypse Now and "the other one"...
Complete the Mile Muncher Challenge
Complete the Ped Popper Challenge
Complete 100 Laps in Death Race
Be the Fox for an hour in Fox 'n' Hounds
Complete the MultiSlayer Challenge
Achieve 100 Cunning Stunts
Complete the Taking the Clunge Challenge
Complete the MP MegaPeep Challenge
Kill 16,666 Peds