The World of Darkness has 4 rooms at the edges.
Each room contains one chest with a Ribbon inside, guarded by Xande's Clone. You should equip each Ribbon immediately whenever you get one.
At the end of each room is a boss, so you'll have to kill 4 more bosses before facing Cloud of Darkness.
Tip 1: Every time you kill a boss, you can examine the dark crystal to fully restore HP/MP and revive your dead allies.
Tip 2: If you cannot kill a boss, you can level up near one of the crystals so that you can restore HP/MP repeatedly. Once you kill the final boss, you'll be able to save your progress, so your leveling will not go to waste.
Bestiary Checklist:
Boss: Cerberus
Besides using normal attacks, he can cast Firaga, Blizzaga, and Thundaga.
Strategy: Use Flare if you have a Black Mage. Otherwise, rely on physical damage. As long as you can out-heal the damage, you'll be fine.
Boss: Echidna
This boss can cast Flare on a single ally, so you can easily lose someone if you're not careful.
Strategy: Go all-out offensively and use Flare back on the boss if you have a Black Mage.
Boss: Ahriman
This boss is weak to Wind. However, it can use both Flare and Meteor, which can easily wipe your entire party.
Strategy: Keep using Curaja every turn to survive its Meteor attack.
Boss: Two-Headed Dragon
This boss doesn't know any magic, but it has extremely powerful physical attacks that can easily kill one of your party members. Be prepared to use a lot of Raise and Phoenix Down.
Strategy: Two members focus on reviving while the other two focus on offense. Don't bother healing after using Phoenix Down - it's usually a waste of turns.
Chests/Items:
- C-364: Ribbon (Monster) - northwest room.
Monsters: Xande's Clone - C-365: Ribbon (Monster) - southwest room.
Monsters: Xande's Clone - C-366: Ribbon (Monster) - southeast room.
Monsters: Xande's Clone - C-367: Ribbon (Monster) - northeast room.
Monsters: Xande's Clone
Boss: Cloud of Darkness
Tell me if this guy ever uses anything other than Particle Beam. Once in a while, he'll use a normal attack and then Particle Beam again - it's just so boring.
To be honest, I just put it on auto-battle with the White Mage casting Curaja every turn. As long as you are not KO'd in one shot, you have a chance to win the battle.
Watch the ending credits and save your game. After it finishes, load your game from the slot you just saved in - you will be placed right in front of the Crystal Tower. Then, you can continue to complete other achievements from there.