Bank any familiars or pets, as you'll be diving in the quest, and it is not possible to do so with a familiar out.
Travel to Mos Le'Harmless, walk a bit north and talk to Brother Tranquility right off of the dock.
Accept his offer to teleport you to Harmony Island.
Run outside and head into the garden, pull the statue and climb down the ladder.
Equip your diving gear.
Go down the stairs.
Run past the zombie pirates.
Repair the stairs at the end of the tunnel, and climb up them.
Then climb the ladder
Peer-through the peephole on the wall.
Make your way back to Brother Tranquility and speak with him.
He'll suggest you get a prayer book that can be used to pray away the poison.
Travel to the monastery near Edgeville.
Search the bookshelves in the southwest corner of the ground to find a prayer book.
floor [ UK] Read the book.
Head back to Brother Tranquility who teleports you to Harmony.
Wear your holy symbol and recite the prayer book by right-clicking on it.
Family Doctor Edit
Talk to Brother Tranquility.
Travel to Dr. Fenkenstrain's abode, which is directly north-east of the Canifis lodestone.
Go up on the staircase in the north-western corner.
Go up on the northern ladder behind the jail gate.
Talk to Dr. Fenkenstrain.
Err... Meow? Edit
Make sure you have at least two open inventory slots, and equip your Ring of Charos (a).
Talk to Rufus, the owner of the meat store, in Canifis.
Travel back to Dr. Fenkenstrain with all of the required items.
Build the crate on the hotspot.
Build a false bottom by clicking the crate.
Click it once again to fill it with fake cats.
Use the wolf whistle to call Rufus.
Use the shipping order on the crate.
Travel back to Mos Le'Harmless.
Head over to Brother Tranquility back on Harmony Island.
Climb down the granary ladder and talk to Dr. Fenkenstrain.
Put on your diving suit and head north from the granary to the ship that had run aground.
Search the locker on the west end of ground floor to get a fuse.
Climb up a level to get a tinderbox and a keg of powder.
Go back to the front door of the monastery and wedge the keg in the front door.
Add a fuse and use your tinderbox on it.
Kill some sorebones until you get the following items:
Go back to the granary and hand those over to Dr. Fenkenstrain.
After the cutscene, go upstairs and talk to Brother Tranquility.
Grab all the armour, food and potions you'll need for the upcoming fight - do not bring a helmet or cape since you still need to wear your diving suit.
Walk through the demolished front door of the monastery to confront Mi-Gor.
After the fight, pick up the anchor.
Inform Brother Tranquility of your victory.