You must get the Red Line Shield on Floor 13, the Balance on Floor 32, and then Hyper Shield on Floor 33.
I didn't bother with the Gauntlets as they aren't required for the hyper shield, but the game might be easier for some. It's your choice.
I used the information provided here to better understand how to make the chests appear on each floor it was pretty accurate for the most part.
https://strategywiki.org/wiki/The_Tower_of_Druaga/Not all items are required but some are absolutely crucial. I'm going to list the items I picked up.
Floor 2: Boots
Defeat 2 Slimes to make the chest appear.Floor 5: Sword (needed to make the other sword upgrades appear)
Block the spells of a Mage with your shield three times while "walking". Movement is not necessary, however, all that is required is to be holding the joystick in a direction. You can be "walking" into a wall while you block the spell (with your sword drawn and your shield to the side of course, or you would not be blocking anything).Floor 6: Candle
Touch the north (top) portion of the outer wall of this floor, then move south.Potions are kind of a waste really (only increasing stamina for that floor), but you can get the blue ones if you really want. Avoid the red ones as they hurt you.
Floor 10: Gauntlet ( I don't remember getting this one but useful if you want the other gauntlet)
Block the spell of a Slime with your shield.Floor 11: Candle Upgrade
Possession of the next Candle grants you the ability to see the ghosts that roam the next few floors, up to floor 15. Unless you collect this, you will not be able to collect the Permanent Candle.
Touch the south (bottom) portion of the outer wall of this floor, then move north.Floor 12: Armor
As with the swords, the armor that you pick up early in the game does little to increase your defense, and only serves as a requirement to collect better armor later in the game. This will allow you to collect the Hyper Armor later in the game.
When a Druid appears in the lowest row of the floor.
Floor 13: Red Line Shield [REQUIRED]
This shield not only increases the area by which a spell will be blocked, this is also needed to collect the Hyper Shield on floor 33 later on.To get it ...
"You have to touch the exit on level 13 then go take care of the enemy's for the chest to spawn.
Thank you @New Paralyzer and @Redstraider
Floor 14: Dragon Potion
Simply wait until the timer reaches 5000.Floor 15: Necklace
As you approach the Blue Knight, draw your sword and pass through him. Sometimes it takes a couple tries, so don't defeat him immediately. Timing also seems to be important. Your sword must just barely be out by the time you pass through him for it to work.
Floor 16: Permanent Candle
Touch the far left and the far right outer walls of the floor.
Floor 17: Potion of Unlock [REQUIRED to beat floor 18]Allow the Ghost to teleport about the floor 5 times.
Floor 18: Sword upgrade
Do not touch any of the outside walls of the floor for between 8 and 12 seconds.
Floor 19: Book of Light [EXTREMELY RECOMMENDED]
Simply open the Door without walking into it. Be sure not to step all the way through the Door and move on to the next floor before you collect the treasure. The treasure will appear in 1-3 seconds.
Floor 21: Ring (I didn't pick this one up but it's useful)
Stand still for any period of time approximately 5 to 10 seconds in length. The sword may NOT be drawn.
Floor 23: Bible (may not be needed but I picked it up in case)
Defeat all the wizards before the slimes.
Floor 24: Balance (for the Gauntlet)
Swing your sword (you can literally tap the button) standing where you started.
Floor 26: Hyper Gauntlet (only if you got the Gauntlet and Balance! If not it will be the Evil Gauntlet which prevents you from drawing your sword; YOU DO NOT WANT THAT!)
The guide I followed mentioned collecting the key then killing a wizard or alternatively kill three wizards before collecting the key, so try either one if you're going for this item. Again, the gauntlets aren't required for the Hyper Shield.
Floor 28: Book [REQUIRED to progress, the real door on floor 29 won't appear without it]Stand on the door and draw your sword (I had to rewind and retry this a couple of times before it worked).
Floor 30: Potion of Unlock (Optional, it's required to open the Treasure on 31, Refer to the screenshot in the link's walkthrough)
Walk over point A or point B (as illustrated on the map) three times. If you walk over point A, it appears you must walk up and down to get it to work.
Floor 31: Pearl (Optional)
Push the start or select button to get it to appear (whichever one isn't pause), that's it.
Floor 32: Balance for Hyper Shield [REQUIRED]
Draw your sword twice in quick succession. This takes a little timing. You should visibly see your sword get drawn and put away twice.
Floor 33: Hyper Shield [REQUIRED of course]
Simply pass through the Silver Dragon. There seems to be a bit more to this, perhaps direction matters, or perhaps the dragon has to be in the center of a square when you do it. (The treasure popped up for me without a problem even though the guide made it sounds like it was trickier).