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