This is an exhaustive list of all the ways through which you can escape Fort Joy.
1. Escape through Fort Joy docks (The Teleporter Quest)
This is the best way to escape fort joy, taking into account the gameplay, fun and fights that you encounter for this escape. You get to know of this escape through a guy named Gawin in Fort Joy Ghetto. Talking to Gawin, if you accept his proposition, open up ‘The Teleporter’ Quest. As a part of this quest, first you will have to fight with crocodiles to get the teleportation gloves which was swallowed by one of them. Once you have the gloves, Gawin will show you a secret location through the Fort joy docks from where you can escape fort Joy by using teleportation gloves.
2. Through the dungeons (Withermoore Soul Jar Quest)
If you happen to find a secret hatch in elven cavern, it will lead to a secret tunnel to Withermoore. He will give you a Quest ‘ Withermoore’s soul Jar’ and also tell you a secret path to Fort Joy dungeon from where you can escape with a boy on the boat. In the dungeon you will have to fight with Magister Houndmaster. And if you are able to save NCP Delorus from houndmaster, he will give you a password using which you can easily escape with a boat boy, Han.
3. Escape using Magister Yarrow’s key
Magister Yarrow could be found on North wall of the fort joy. She gives you the Quest ‘The Murderous Gheist’ . Completing the quest may have two outcomes –
1) Yarrow gives you the key
2) You kill Migo and Yarrow does not give you the key.
If your outcome is the second one, then you can kill Magister Yarrow and take the key from her dead body.
You can use Magister Yarrow’s key to enter Magister Quarters, which is located south of the main gate leading inside the fort. Ladder leading to the door is propped up. You have to use teleportation gloves to send someone to the catwalk and drop the ladder. Then use Yarrow’s key to get inside the Magister’s Quarters.
In the next room, you will come face to face with High judge Orivand. You have to first kill him to escape fort joy. Once you have won the fight, escape fort joy by using the ladder in the circular room at the corner.
4. Escape through secret tunnel containing fire slugs (Freeing the Elf Quest)
The hatch to enter this secret tunnel is on the beach where you fight Migo. Amyro gives you the location of this hatch is you complete the Quest ‘The Imprisoned Elf’. This secret tunnel containing fire slugs lead you to the Fort Joy dungeon. In the dungeon you will have to fight with Magister Houndmaster. And if you are able to save NCP Delorus from houndmaster, he will give you a password using which you can easily escape with a boat boy, Han.
5. Escape through the fort main gate
This is the most straightforward method to escape fort joy.
When you are at Fort Joy ghetto, there is heavily guarded gate leading into the Fort . Fight with the Magisters guarding that gate and after defeating them take key from the dead body and open the gate to enter the Fort Joy.
After entering fort Joy proceed towards the main gate of Fort Joy. Here again you will have to fight a few Magisters. Another NCP named Paladin Cork is fighting the Magisters here (Saving him earns you extra xp, but even if he is killed there is no impact on the game)
After the Magisters are defeated lower the drawbridge using a lever and escape fort joy through the bridge.
6. Escape Fort Joy through the sewer
There is a sewer in Fort Joy Prison that lead to the swamps outside Fort Joy area.
The sewer is in the torture chamber of the Fort Joy Prison. You can reach enter the prison through the dungeon or through the door in Fort joy courtyard (Both covered in previous methods of escaping). In order to escape through this sewer you will have to fight with Kniles the Flenser. Once you have killed Kniles, you can escape through the sewer which is at the corner of the torture cell.
7. By winning the Fort Joy Arena fight
After winning the Fort joy arena fight you can get your collar removed. If a Magister sees you without your collar, it starts a conversation which leads either a fight or you going into the dungeons. Once you are in the dungeon follow the steps in point 2 above to escape on boat with a boy.