This can be found all over but I will explain a few things not covered by this image alone.

As you may have seen, once you progress past a certain point in the story you are afforded the oppurtunity to enter any item and make its effect stronger by killing hostiles within.

Each item has a few unique properties. As you progress through the floors you will pick up all kinds of bonuses and kill thousands of enemies. Each enemy you kill adds a small bonus upon the item after you exit making it stronger. You will notice on the image chart that each item has a type, and a rank.
What you are likely shooting for is the rank 40 weapons, armor, Shoes, and treasures. Thing is you are likely not going to want to grind out ~40000 floors for all this, I assure you there is a better way.

Hidden among the troves of information out there on this game is a method that helps with aquiring items close to where you wanna be in the chart. What you are looking for are Rank 39 items, sometimes you might settle for a rank 38 item if your patience is running thin. Thing is the Pocket world shop i think caps out at like rank 24 or so, hardly even close. Stealing from end story characters can get you in the low 30s but you can do better.

The eringi (mushroom dudes) have an evility that when hit they make a comsumbale item called Mushroom soup. That is a rank 39 item. Thing is its relitively low chance of occurance, further hindered by the fact you dont always get soup.

Once you have your Rank 39 item you want to jump into its Item world. Its important that its 39, It doesnt have to be the soup but the soup is probably going to be the fastest way to get there.

Once in the rank 39 item, the enemies will be equipped with various gear that commonly ranges from rank 35 up to the rarely rank 39. The thing about the soup is that everything is available here. You will see a LOT of junk but soon you will start to see the items you are looking for.

Once you see your R39 item go ahead and steal that sucker.

Theifs annoy me personally. They are squishy and dont really fit well in my play style. I love to Cross Class Artina into a thief though.

There are a few skills and abilities that are unique to Theives.

Theif Skills Evility.
This is the Unique Evility Specific to theives. This allows them to steal at 99% if their stats allow.
Theif Subclass will need to be mastered in order to plug this into a character that isnt a Theif
where as Theives come with this default.

Lucky Finger
This is a common evility for theives that increase the item rank of an item by 1 when they crack a chest. Here is the kicker though... the best you can get is 39 so dont think you can be sneakey and pop a genesis wand out from a chest.

Phantom Angel (Artina)
This is why i like to make Artina my theif. Whenever she steals something, Anything she kicks up the rarity of the item by 20. Keep in mind this has little to do with the item rank, but it basically gives the item a head start on its growth when you do get your hands on it.

Arrow to the knee (Archer)
This evility lets you get the effect of SPD down on bows like guns do naturally. You may or may not care for this. I personally rather not risk killing my target before i get the loot im hunting for. The good news is even if you do 0 dmg you still lower the spd.

So last but not least, how to theif!

Its all in the stats baby. There are some great guides here on how to get them stats up but to theif you are looking for HIT. You want that as high as you can get it, and your target, they need LOW speed. Another reason why i like Artina is that she is typically a healer, so it would make sense to teach a few buffs, Specifically Target Lock (Asagi learns this), That can give you a critical boost to hit and if you boost RES first with Magic Barrier, which Artina learns naturally, your next cast of target lock will have a little more kick to it.

Now since Artina is not a theif she will not have Steal item skill. So you will have to use the Hand items which can be purchased at the store.

With all that said lets talk about stats. Normal mode natural stats will likely cut it with little effort. You can probably steal anything with as little as 250K Hit.
Carnage mode is far less forgiving.
10 million is the minimum you will need to have any success at nabbing anything Rank40.
15 million and the spells can get you comfortable.
20 million and you should not have any trouble anywhere.

You may notice that there is more than one R40 weapon. This is the thing i had to learn the hard way.. Twice..

So as you progress the item world, you will run into mystery rooms. Very rarely you will find this one.
Here is the thing that is not often known. It behaves differently in Carnage than in Normal dimention.

I know it says so in the chart but there is something missing and a TON of speculation and misinformation on forums and Gaming sites. Ill come back to that in a minute.

First Like it says in the chart if you hit this room all you need is someone that has weapon master lvl 40 to grab it in normal mode. To be clear this is weapon mastery:
Here you can see Staves and Bows are Capped out. So i can nab a Bow and staff all day long in ANY bow or staff item in normal. Yes this room can pop up in a driftwood bow just as easily as it would in a Divinity.

Now comes the skrew ball. This made me chuck many a controller hunting in carnage. That image above clearly shows lvl 100 bow and staff. So you would think if im in a R39 Majin Greatbow grinding up to a Divinity that if i happen to stumble upon this mystery room i should be able to walk away with a Artimis.

You would be frustratingly wrong.

The answer is you actually need not only the 100 weapon master but you need to have the Divinty as well or the corosponding Rank 40 weapon aquired from the Item God2 or the R40 from reasearch. The Maijin great bow(R39) will tease worse than a school girl and it will seem like this mystery room pops up every three floor clears just to play with your emotions more and more if you do not have its corrospnding R40 item already.

The Arcadia, Trap, Herc, Vthruster, BarfootX,and aegis sheild wont play with you like that because this mystery room does not show up there, Only in weapons.

The Last rank 40s are aquired through Nether Research. This is an activity i dedicate very little resources to but that is foolish of me.

These items are very powerful and stat requirements are more aggressive than the item world.
What you are looking for is Rank limit that is Greater than or equal to 40 Red Rank limits are Carnage Items White are normal.

Again Normal is very chill and forgiving. You will need very little preperation to handle it, and could probably get away with natural progression.

But you are not reading this guide because you are casual. You will settle for nothing less than perfection!!!

So on to carnage demention. As you will see in the circled Green number that is the recommended level you send your research sqaud be. If you are like me you will be tempted to chuck your trash characters out there, though if you were to do that they would get creamed. That number is terribly misleading. Further more that is where Carnage starts... It gets worse. You will need to train your trash toons to ship out as well. The good news is some of those trashy overlords you picked up chasing the boss of the story can be easily leveled using Magichange and a decent sage..

The bad news is that is just to Find the Rank 40 world. Once found, you have to research it, and hope the Overlord calls you out and lets you fight.

A fight he will happily give too. The R40 Overlord make item gods look like prinnys. Your 20mil stat toon will be actually taking damage in this fight and too many licks and you are out, worse yet, the overlord will ROFLMAO so hard his world blows up and you have to find a new one. With all that said you will want at least 5 guys decked out in OTHER R40 gear with average stats 20 mil or more each.