Go to Tonfon. Enter the palace. Outside of Lady Hinechou's room you will see a gong. Use Slap Psyenergy on the gong. Everyone will go outside. Go inside and upstairs. Check the closet, and you will get the Echo Gem. Follow the signal generated by the gem, to the Snowdrift Shrine (it's west of Harun Village). There you will find Hou Zan, Ryu Kou, and Hou Ju. You will receive a map of where the Umbra gear is.
Crossbone Isle: This area contains 2 summons (Charon & Iris), Iris is guarded by the the hardest boss in the game, Dullahan, and various items. To get there, go directly south of Tonfon, until you reach a whirlpool. Go into it, then head east.
These areas are already there before, but some require the Sol Blade to get further into them:
Burning Island: Contains 1 summon, 1 boss (Or five, depending on how look at it), 1 djinn (Flare), and a piece of the Umbra gear. Go south of Champa until you reach an island shaped like a spiral. Requires Sol Blade to reach boss.
Otka Island: Contains 1 summon (Coatlique), 1 boss (Ancient Devil), 1 djinn (Lull), and various items. While sailing around Yamata, you may have seen a tornado (Or heard it). Enter that tornado. Requires Sol Blade to reach boss.
Lost Ship: Contains 1 summon (Azul), 1 boss (Star Magician), and various items. Look north of Harun Village, until you find a rock shaped like a hand. Go left of that, into the eclipsed cloud. You will be taken onto the ship.
To get access to the final optional dungeon you must defeat the final boss and save your game after the credits. Reload the cleared saved game file and sail south from Tonfon until you reach a 'C' shaped peninsula at the edge of the world. Enter the whirlpool at that location and sail east from the exit until you find an island with a cave. This cave will lead to the entrance of Crossbone Isle which is the hardest boss of the game.