This is a very time consuming achievement so I recommend leaving it for last.
The first thing you want to do is start a new cycle. The reason we do this is because when you Discipline for Treasure the Treasure spawns on any cleared Stage. Since we are starting a new cycle we can control what map the treasure spawns on by only clearing one map. We want an X-Dimension map because it seems like the Treasure parts have a higher chance of appearing.
You will need access to the X-Dimension Stages which if you are leaving this for last, you should have the Promotional Tickets already. I recommend clearing Stage X-10-6 Boiling Point. The Treasure is accessible from the start and can easily be cleared in one turn with a Magician DO NOT
Clear any other Stages including regular Stages.
Next head to the Cheat Shop and set the Enemy strength to LVL 20.
Now head into the item world in a Legendary item and get to about LVL 40. This is when you should be seeing LVL 9999 enemies, higher level enemies tend to have higher chance of spawning Ship Parts. From this point on use your team to capture 16 enemies to torture. I will have a link below to the Disgaea Ship part wiki which has the parts and the enemies you have to torture below. Once you are full you will be told you cant throw an enemy into the base panel because its full of hostages. Sometimes the base panel will get destroyed and sometimes your allies inside will die. At that point just move to the next floor or gency out and heal.
Once you have your 16 captures. Gency out to the base and start to discipline. SAVE YOUR GAME BEFORE ASKING FOR TREASURE. Head to the map the Treasure spawned on and open the chest. If you get a Ship Part, complete the level. If not, Quit to Title screen, reload and ask for treasure again. Once you got the ship part release the hostage and repeat for the rest of them.
Be sure to keep a list of the parts you need so you dont waste time capturing enemies that dont have parts. Also take advantage of Mystery Rooms. They will reset the current map if theres no one you need to capture or you can get take to the Lottery Mystery Room with a Gargoyle Selling Release\Unlock and X-Tickets. These tend to spawn Ship parts as well. Just Save before using each one to make sure you get a ship part each time.
Here is the Link to the Disgaea Wiki. https://disgaea.fandom.com/wiki/Pirate_Editor
I did not create this Wiki. I take no credit for it. I should warn that I believe its missing the part "Infinity" which is a R and L arm part.
EDIT: Thanks to JDuke705 for pointing out the Infinity Piece was acquired from a GunnerDisciplining
To Make things easier I will list the easiest way to Discipline enemies. You want Valvatorez, Fenrich and Valkyrie as you Allies in the Discipline Evil Symbol as these 3 Characters cover ALL weakness. Below is the following Discipline options to choose and who its effective on:Tie Their Wrists (Default):
Skull, Witch, Cleric, Sorcerer, Professor and Onmyo Monk.Loyalty Training (Fenrich):
Warrior, Valkyrie, Ninja, Lady Samurai, Beast Master, Masked Hero, Prism Ranger (DLC class), Kunoichi (DLC class), Medic (DLC class), Necromancer (DLC class), Winged Warrior, Slumber Cat, Prinny, Roc (Cocatrice), Mystic Beast and Death Saber (DLC class).Forced Massage (Valvatorez):
Flora Beast, Succubus and Felynn.Unnecessary Favor (Valvatorez):
Archer, Gunner, Armor Knight, Thief, Bouncer, Battle Suit, Android, Orc, Gargoyle, Dragon Zombie, Wood Golem, Dragon and Rifle Demon.Go Travel (Valkyrie):
Magic Knight, Celestial Host (DLC class), Sludge, Shroom, Spirit, Undead, and Death.
There is another Error to bring up, The Treasure Ship Body is NOT aquired from a Thief. Its actually acquired by defeating the Peachboy Pirates. I will add extra info on this as Spoiler if you would like to check it out.Item World Routes and Pirates Guide