When you begin, do so by grabbing yourself (the real you) a piece of paper. Having the Charm Bangle equipped will also be helpful in eliminating variables. You’ll notice “No Data” in the topleft part of the screen, and “[_] > ##” in the lowerright. This will be important later.
Open one of the two chests that appear. Open either of them to get a brief tutorial on navigating the cave. It basically works as follows:
 All info for unlocking the next wall is in the topleft and bottomright of the screen, and it is displayed upon entering the cave and examining walls.
 You can press Square to review this information three times between unlocking walls. The topleft  initially “No Data”  will be the CURRENT wall number, and the bottomright the number of the next wall. Be sure to note these every time!
 When you examine the next wall you need to open, you need to input a number. This number will be equal to the sum of the topleft number and the bottomright number (current and previous doors) you were given earlier. However, they’re not necessarily the numbers of the doors: maybe battles fought? Maybe Gil earned? Whatever is readily observable.
 Two chests appear beyond every wall. One is a clue, and the other is empty.
Some further tips are given beyond this tutorial:
 We’ll begin by examining the message we first saw upon entering the cave. Press Square to do so; it’s basically an explanation by example.
 The number in the bottomright is the “next wall” number. Note that the key number is six, and the wall number is 3.
 The map in the topleft will show your next number (or the walkthrough will). Yuna will head to Wall 3 automatically, but you must learn to do so yourself.
 Examine the wall with X.
 The second number in the topleft corner is the first Key Number for Wall 3. (2 in this example.) Remember, earlier we saw the second Key Number for Wall 3 was 6. 2 + 6 = 8, so the input of 8 allows you forward.
 After going forward, take note that the Key Number in the lowerright changes (here, to 20 for Wall 10). Keep that in mind and on your paper.
 Also open the chests.
They will never be constant between any two playthroughs: how to get the number, usually it’s not random, but the number itself is. One will always appear when you get to the wall you need to open, and another when you’re on the way there. Also, be sure to note the distinction between “since entering the cave” and “since the last wall” when it comes to the amount of battles/Gil you need to use.
Next Wall  Wall 3:

Where ?: You should’ve done this one in the tutorial.

Numbers ?: Random for both, but from previous walls’ clues.
Next Wall  Wall 10: 
Where ?: Go south and along the path for a bit from #3, then go west and north at the intersections; it will be on the west side. (Before going north, go west for Diamond Gloves .)

Numbers ?: Random for both, but from previous walls.
Next Wall  Wall 11: 
Where ?: Grab the Hyper Wrist in front of you, then go south. Grab the Battle Compendium to the west at the insection, then go far to the east for the Code Compendium . Go north and east at the intersection for a Mystery Veil , then west to the door.

Numbers ?: Two random again.
Next Wall  Wall 5: 
Where ?: South now, then east for a Talisman . Go west past the twoway, then north to the wall.

Numbers ?: One is random, one number was previously used.
Next Wall  Wall 1: 
Where ?: Go west and you’ll find it.

Numbers ?: One number was previously used. The second was the number of battles between entering the cave and opening any walls (0 with a Charm Bangle).
Next Wall  Wall 8: 
Where ?: When you go south of #1, you’ll be at a twoway; go east, then south, then west and along the path there to find a Nature’s Lore . Return to the intersection just south of #1 and go west, then south, then east to find it.

Numbers ?: The first is an alreadyused number plus the number of battles since entering the cave. The second is random.
Next Wall  Wall 12: 
Where ?: Go due south of #8 and head east at the second intersection you reach; it’ll appear to the south.

Numbers ?: The first is random. The second is an old number plus another old number.
Next Wall  Wall 13: 
Where ?: Go east for a bit in the hall after dealing with #12; it’ll appear to the north.

Numbers ?: Both are random.
Next Wall  Wall 9: 
Where ?: Go east from #13 in the hall north of it, then go north for a while when first possible.

Numbers ?: The first is an old number. The second is the number of battles between this wall and Wall #12.
Next Wall  Wall 6: 
Where ?: Simply go west and north.

Numbers ?: The first number is an old number plus a random number. The second is the sum of two old numbers.
Next Wall  Wall 7: 
Where ?: Go east a bit. Grabbing the Gil Compendium might be a good idea now.

Numbers ?: The first is the amount of Gil earned since coming into the cave (0 with a Charm Bangle). The second is the sum of an old number and the battles since opening a wall.
Next Wall  Wall 14: 
Where ?: Begin by going west, south, and east from #7 to find the Corpus Invictus . Anyhow, this wall is in the southcentral portion of the area, between where #12 and #13 were.

Numbers ?: An old number is the first, and the sum of two old numbers is the second.
Next Wall  Wall 2: 
Where ?: East of where #1 was.

Numbers ?: The first is the number of battles between opening this and the last wall. The second is random.
Next Wall  Wall 15: 
Where ?: Head north from where #14 was.

Numbers ?: The first is sum of the two random numbers given plus the Gil earned since the last wall. The second is the sum of an old number, the battles since the last wall, and the Gil since entering the cave.
Next Wall  Wall 16: 
Where ?: Keep going north. Grab the Salvation Promised Garment Grid on the way.

Numbers ?: Two random ones.
There’s nothing special other than the indungeon treasures for the first time, but…there is a reward for finishing the dungeon twice! The numbers used will not be the same. You’ll get the Force of Nature accessory for finishing the second time.
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