Here is the full list of all 51 Post Apocalyptic Mayhem achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Finish in 1st place in Ranked Multiplayer mode with 5 human opponents.
Kill a total of 100 opponents in Arcade 'Medium' mode.
Finish in 1st place in every race in Apocalyptic Challenge 'Medium' mode.
Kill 15 opponents in one race in Arcade 'Hard' mode.
Finish in 1st place in Arcade 'Hard' mode.
Score 15,000 points on the 'Concrete Jungle' track in Arcade 'Medium' mode.
Finish in 1st place in Arcade 'Medium' mode.
Finish 3rd or higher in Arcade 'Medium' mode.
Kill 10 opponents in one race in Arcade 'Medium' mode.
Complete an Apocalyptic Challenge.
Score 25,000 points in Apocalyptic Challenge 'Easy' mode.
Drive the 'The Veteran' in Arcade mode.
Kill a total of 100 opponents in Arcade 'Easy' mode.
Score 15,000 points driving the 'Nucloid' in Arcade mode.
Finish in 1st place driving the 'Kitty with Claws' in Arcade mode.
Getting at least one kill with all three of any vehicle’s weapons in Arcade mode.
Complete 2 laps in the 'Wasteland' track in Arcade 'Easy' mode.
Finish 3rd or higher in Arcade 'Easy' mode.
Finish in 1st place in Arcade 'Easy' mode.
Kill 5 opponents in one race in Arcade 'Easy' mode.
Use any ability to kill an enemy in Arcade 'Easy' mode.
Score 20,000 points driving the 'The Veteran' in Ranked Multiplayer mode.
Kill an online enemy (not an AI vehicle or a Friend) 5 times during one race!
Complete 2 laps in the 'Cold War Beach' track in Ranked Multiplayer mode.
Score 15,000 points in Ranked Multiplayer mode.
Finish in 1st place in all 3 of the 'Death Area 8' vehicles in Ranked Multiplayer mode.
Score 15,000 points in the 'Death 8 Area' track in Ranked Multiplayer mode.
Complete 20 clockwise laps around Santa's house without ramming into anything.
Finish the holiday track in first place.
Use only one of vehicle’s weapons to kill opponents and finish in 1st place.
Kill an opponent in the air on the holiday track.
Drive the 'Nucloid' in Ranked Multiplayer mode.
Drive the 'Kitty with Claws' in Ranked Multiplayer mode.
Kill an enemy within 30 seconds after he has killed you in Ranked Multiplayer mode.
Kill two enemies within 5 seconds in Ranked Multiplayer mode.
Finish in 1st place in Ranked Multiplayer mode.
Lap your opponents, sneak up from behind and kill the straggler!
Gang up with one of your friends to attack and kill an opponent!
Race the holiday track.
Find Santa’s secret hideaway.
Adjust a Tuning Slider and save the new setting.
Use a suicidal crash and no weapons to kill an enemy in Arcade 'Hard' mode.
Kill a total of 500 opponents in Arcade 'Hard' mode.
Get at least 5 kills in Ranked Multiplayer mode using every weapon for all vehicles.
Finish in 1st place on every track in Ranked Multiplayer mode.
Kill a total of 100 opponents in Arcade 'Hard' mode.
Kill a total of 500 opponents in Arcade 'Easy' mode.
Kill a total of 500 opponents in Arcade 'Medium' mode.
Score 40,000 points in Apocalyptic Challenge 'Hard' mode.
Kill 500 opponents on the holiday track.
Accomplish all the holiday achievements.