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