Here is the full list of all 33 Party of Sin achievements.
Complete all levels with four stars
Purchase all the sin upgrades
Purchase all the cheats
Defeat the Archangel Michael
Defeat "Total War" without dying
Complete all levels with three stars
Complete all levels with two stars
Defeat the northwest door of the cathedral without dying
Collect all the green apples in the adventure
Defeat the northeast door of the cathedral without dying
Defeat the southeast door of the cathedral without dying
Defeat "Crash Landing" without dying
Defeat "Sky Pirate" without dying
Defeat the Airship Captain Luriel
Defeat "Take Off" without dying
Defeat "Windopolis" without dying
Defeat "Emergence" without dying
Defeat an Angel Commando
Defeat a Templar Warrior
Defeat "Overseer" without dying
Defeat the Purgatory Overseer
Defeat "Ovenblast" without dying
Defeat a Shield Angel
Defeat "Badlands" without dying
Defeat an Angel Priest
Defeat "Arachnid" without dying
Defeat the Demon Spider
Defeat "Damn Dam" without dying
Defeat "Tortoise Port" without dying
Defeat the Demon Narwhal
Defeat "Trench and Slide" without dying
Defeat a Warrior Angel
Defeat a Demon Guard