Doppelganger is the final boss in Ghost Ship Extreme. After you have finished the regular Ghost Ship, return and speak to the ghost named Minoc near its entrance and pass his quiz to gain access to Extreme. If you've reached this point in the game, you don't need advice on how to fight, but I will tell you a bit about this dungeon to perhaps save you some trouble.
Ghost Ship Extreme has 100 floors. Each floor has four elevators marked by yellow dots on the map, only one of which works. It's your job to find the the one that will take you up to the next floor; the red crystals around the working elevator will be lit up. The non-working ones are dark.
The most important thing to keep in mind is that if you leave the dungeon at any time, you will have to start back at the beginning when you return. You'll notice that you can't connect to other teleporters in there. You can only teleport out, so be sure you have everything you need before you go, including healing items, weapons that you want to build up (if you're working on the Seven Star swords), etc.
There are enough teleporters around that you can stay healed up without using all of your supplies. You'll hit a boss every ten floors, and there are three shops - one each on Floors 30, 60, and 90.
Since I'm not worried about completing the Hunter's Log, I moved through here pretty quickly, and it still took me the better part of two days.
Good luck!