Here is the full list of all 34 The Chaos Engine achievements.
Clear world 3, The Fortesque Mansion
Kill 500 enemies in a single play through
Clear world 2, The Workshops
Use a first-aid kit 50 times
Use 50 Specials from your inventory
Kill 20 enemies in a single run without losing any health
Clear world 1, The Forest.
Kill your first enemy
Destroy the Chaos Engine
Destroy the Chaos Engine with 2 players alive
Collect 10000 money in a single play through
Fully upgrade the Brigand character
Fully upgrade the Gentleman character
Fully upgrade the Thug character
Fully upgrade the Mercenary character
Fully upgrade the Navvie character
Fully upgrade the Scientist character
Use the Molotov Special from your inventory 50 times
Use the Shotburst Special from your inventory 50 times
Use the Ground Mine Special from your inventory 50 times
Use the Bomb Special from your inventory 50 times
Use the Dynamite Special from your inventory 50 times
Use the Freeze Monster Special from your inventory 50 times
Use the Distract Monster Special from your inventory 50 times
Fully upgrade a single statistic for any character
Find 28 gold keys in a single run
Complete the campaign in a single run
Die 100 times
Resurrect 10x dead characters in co-op games
24 hours played in total
Complete single-player campaign playing as all six characters
Reach Game Over with less than 1000 score
Kill 500 Frogs
Collect 50000 money