The Ice Cavern is located on the southern wall of the Gunitas Basin on the Mist Continent. It is located directly south of where the party exits the Evil Forest. Use the map and the screenshot below to help you find the location.
Zidane, Princess Garnet, Steiner and Vivi will stop outside of the Ice Cavern for a quick break to discuss the path forward. Vivi will explain that his Grandfather mentioned that the cavern can be used to reach the top of the Mist. After the quick discussion the team will head on inside.
There are small bits of mist that will spray out of various holes in the side of the cavern. Touching the mist will automatically trigger a battle so make sure you cross them carefully and only move over them when the mist is not blowing through.
Move towards the ledge on the left side of the screen with the treasure chest on it and press the 
Button to climb up. Open the chest to pick up a 
Tent. Climb up to the next ledge and head down the pathway into the next area.
On the right side of the screen is a “strange wall” blocking the path. Vivi will use his Fire magic to remove the wall. The treasure chest hidden behind it contains an 
Ether.
There is another treasure chest on the left side of the room that you can reach by taking the pathway to the right of the stairs leading up.
Take the pathway around behind to get to the left side of the screen and grab the chest to retrieve a 
Potion. Track your way back to the stairs and proceed towards the far end of the pathway into the next screen.
There is another ice wall that Vivi can break at the back-left corner of the room. The treasure chest hidden behind it contains an 
Elixir. Towards the bottom of the screen is a log on a pathway that leads to another chest containing a Potion.
The question mark icon will appear near the base of the log/icicle - have Vivi use his Fire magic on the log to cause it to drop down. This will allow you to access the treasure chest on the lower level which contains a 
Mage Masher (in case you didn’t steal one from Baku/Masked Man at the beginning of the game). Proceed to the northeast corner to continue into the next area.
The pathway on the right side of the room has a treasure chest out in the open - it contains a 
Phoenix Down. Walk over to the left side of the screen to find a doorway blocked with ice. Have Vivi use his Fire magic to open the pathway which leads around to a 
Leather Wrist.
You should equip this equipment on Vivi as this wrist armor can teach him 
Blizzard magic. Head north to the next area of the ice path.
The next area has a fork in the road - the pathway to the left leads to a cave with a frozen Moogle named Mois. Having Vivi unfreeze him will automatically trigger an Active Time Event (ATE) taking you back to the two Moogles talking at the swamp. This time they will teach you about a number of new topics including Save Moogles, Status Effects, Elemental Properties and the Card Game.
Speak to Mois and save your game. Speak to him about Mognet as well and he will give you a letter from Mois to Gumo. Head back south to the fork in the road and take the right pathway this time to the next boss.
Black Waltz 1
Level: 2
HP: 229
Sealion
Level: 3
HP: 472
This fight will only include Zidane. Make sure that you steal the 
Mythril Dagger from Sealion before ending the fight as it is an incredibly powerful weapon that can teach Zidane the 
Bandit ability to improve his chances of successfully stealing. The other items which can be stolen from the Black Waltz 1 are of limited value and are not necessarily worth taking the time to steal.
Make sure to keep Zidane healed up and by the time you need to deal any damage to Black Waltz 1 or Sealion he will likely be in a Trance. Zidane’s Tidal Flame Dyne attack deals massive damage to these ice-elemental enemies.
Sealion’s attacks are based on the color of the orb sitting at the center of its body. Sealion can only use a regular attack move when its orb is blue. It can use its regular attack and cast Blizzard spells when the orb is yellow (which hit for around 35 damage).
It can use both regular attacks and Blizzard as well as a move called Tsunami when the orb is red. Tsunami can hit for around 80 damage. Don’t do any damage to Sealion until you are ready to defeat it as changing the orb colors early on can make the fight very difficult.
Steal (Black Waltz 1):
Remedy (common)
Silk Shirt (uncommon)
Steal (Sealion):
Ether (common)
Mythril Dagger (uncommon)
Drops (Black Waltz 1):
Hi-Potion (common)
Drops (Black Waltz 1):
Phoenix Down (common)
A video of the battle is included below:
Head towards the back of the cave and up the ice walkway after the battle has concluded. There is a short scene at the exit of the Ice Cavern where Princess Garnet will come up with a fake identity for herself. You’ll get the opportunity to rename her character both in the game and on the battle screen.
The default character name for her is Dagger and she will be referred to as that throughout the remainder of this strategy guide (sometimes intermittently with ‘Princess Garnet’).
There are a couple of optional areas that you can visit before continuing with the main story. The first area is called the South Gate / Dali Gate which is located through the forests to the north from the exit of the Ice Cavern.
There isn’t much to see at the South Gate though. You can’t pass through without a Gate Pass which you do not have yet. You are given the option to “take a break” though which will require you to wait for the shop girl named Vega. She takes about 10 or 15 seconds to show up after you tell the guard that you wish to wait for her.
Speak to her and you can choose to rest for 100 gil (refilling your HP and MP) or to buy items from her shop. She sells the following items:
Potions (50 gil)
Phoenix Downs (150 gil)
Antidotes (50 gil)
Eye Drops (50 gil)
Tents (800 gil)
There are two structures to the west of the Ice Cavern exit. The one on the right is the Observatory which is another optional area you can visit.
It is possible that you may run into a friendly monster in this area named Mu. This creature will ask you for an 
Ore and is part of the Friendly Monsters side quest. Click on the link for more information.
Tracking down Mu and completing providing it with Ore will reward you with a free Potion and 10 AP, which is a great reward to help your characters finish learning some of their abilities.
This area is involved in a side quest that you can complete later on in the game but there are a few items that you can pick up on your first pass through the area right now.
Near the cart at the front entrance is a hidden Hi-Potion. There is also a hidden stash of 135 gil behind a rock towards the back-right side of the screen.
You can initiate the side quest for this area by entering the house and examining the small model of the flying ship hovering over the bed. Morris will ask you to help him find some rare coffee in exchange for the ship (the three coffees that he is looking for are Burman, Kirman and Moccha).
That’s all that you can do at the Observatory for now. You can also check out the Rare Coffees side quest section for more information on this side quest (which you can complete later).
Your next destination is the town of Dali.
