Ring of Pain

The Gear

- Double Candle
- Hermit's Tiara
- Weightless
- Polearm

The Stats

-Speed
As with every Tiara run this should be your main priority. Get 21 as soon as possible and aim to keep it there.
-Health
The only damage you should be taking is emergency stealth attempts, bile bags and hidden spine backs after getting Polearm. You may also need to tank a ranged hit from Owl. Rush bile bags and the rest can be avoided with careful planning and movement. 25 - 30 is fine.
-Attack
In theory you could do this with 0 or less attack if you have the patience to beat Owl 1 health at a time. Get it high enough to deal with potential blockers in the final fight and anything more is a luxury/time-saver. I finished with 14 and managed fine.
-Clarity
Not a big deal. Just keep it above 0 for emergency potion use and extra soul gain.
-Defense
High speed + Polearm makes defense entirely pointless. The baby loombirds in the final room and Wretched Amalgams you don't kill early are the only things that will be fast enough to hit you at 21 speed. You'll have the Polearm in the final and should rush Amalgams whenever you see them. The rest of the damage you'll receive bypasses defense anyway. Like Clarity, try and have it above 0 for the final fight but don't stress too much.

The Run

-Dungeon 1
Pick Double Candle and start with Hermit's Tiara. Clear the room and empty the chests, rerolling until you get Weightless. If you don't, restart. Weightless gives you +7 Speed from the start, allowing you to get to 21 faster and giving you room to upgrade other stats.
-Dungeon 2 - 13
Kill everything. Prioritise Scroungers and get every stat card, including cursed ones. Take as many side rooms (except Chills) as possible to maximise Souls gained. Make sure to go into Reprieve and kill Owl to weaken him for the final fight.
-Dungeon 14 - 16
Gold chests should be spawning now. Crack open the first one and reroll until you get the Polearm. If you spend all of your souls in Room 14 there is a possibility you get enough to have one more go in Room 16. This is pure RNG, it took me 4 runs to get a Polearm.

The Boss

First off you should freeze the enemies closest to you and kill any scroungers. The plan is to stack the ring with ice cubes and neutral cards. The ideal position to be in when he reaches you is;
Owl > frozen enemy or neutral card at front left > neutral card at front right (or the reverse if he comes at you from the right)

Now all you have to do is hop over the front left card and damage Owl with the Polearm and then hop back to the right away from him. Repeat this until he goes back into the middle. Avoid his ranged attacks and freeze more enemies on your way to destroying a candle to force him back into the ring.
You can either play safe and wait for him to come to you, freezing more enemies while he's stunned or go to him to get in some free shots. Either way you should revert to the tactic of hopping over a card to hit him with the Polearm and hopping away until he goes back to the middle.

He will occasionally spawn more enemies. These loombirds can make things complicated and you should aim to Polearm Freeze them in the baby phase so they don't transform to track you down, which may end up with you pinned between Owl and a Loombird, forcing you to tank a hit as you escape past the weaker Loombird.

All that's left is to repeat this dance until he's dead which will take at most 1000 turns if you decided to not upgrade your damage and not kill him in the Reprieve Dungeon.

You will also unlock

I tried the helpful solution provided by james bogart. I think the initial setup of that guide is great and the way to go. However, after numerous attempts I always seemed to get stuck at the final fight, either being trapped by Loombirds or blocked by a Shackle while not having high enough attack power to clear a path in time before the owl cornered me.

I finally managed to get the achievement with an alternative setup for the final boss. Keep in mind that it is very much RNG and therefore luck-based:

STARTING GEAR
- Double Candle (pick Hermit's Tiara as starting gear)
- Weightless

When you start the first round and you do not get Weightless, restart the game. It takes around 1 minute to clear the first floor. Repeat until you get it.

STATS
Get you speed to 21. In case you get a stat boost where speed is not an option, choose to increase attack or life points. I aimed for life around 30 and put everything else in attack. I tried to keep defense neutral or slightly negative (-1/-2). Clarity I tried to have around 8.

SOULS
The goal is to collect as many souls as possible so that once you reach the legendary gear (golden chests) you can reroll more so that you have a higher chance to get the desired gear. For that you should always try to clear all enemies (except for monsters resistant to ice). In addition, always try to choose alternative paths, preferably those that involve combat. Even the path Chills I would recommend to take if you can manage 1-2 hits and it is the only alternative path available. Normally, the Chills path spawns two minion ice monsters and 1 boss ice monster.

SCROLLS
- Soul craft (rarity: purple)
Destroy an equipped item. Gain its primary stats and Soul cost

You have to be lucky to find the scroll Soul craft, which does not spawn very frequently. Once found, you should remove Weightless to get its stats and have a slot available for more powerful gear. Please note that it is not possible to remove Double Candle with Soul craft (I tried).

- Final form (rarity: yellow)
+1 to all stats and +5 Splash Damage for this Dungeon

Sometimes it happens that you come across this scroll at one of the last floors. If you can, save it up for the final fight with the owl. At this point, you most likely have 5 items equiped when carrying the scroll so you will have to fight 1-2 floors without the freezing power of the Hermit's Tiara.

END GAME GEAR
After removing Weightless with Soul craft, you should have two open gear spots. You need the following:

- Bolster (golden chest)
Item gains +1 to all primary stats for each empty inventory slot

This will be a huge stat boost and will help you power through the boss battle.

- Banishing Mace (golden chest)
Attack targets get randomly teleported

This will help keeping the owl at a distance. This does NOT avoid the attacks of the owl but it keeps the boss at a distance and your stats should be high enough to take a hit. One melee attack of the owl is 30 damage. His ranged attacks are 15.

THE BOSS
The idea is to always keep one passive card between you and the owl. Keep the following in mind:
- Never create a situation where you have a loombird at one side and the owl at the other. The same applies to a Shackle and the owl.
- Try to avoid the owl's ranged attacks. The ranged attack either take two turns (two targets) or 5 rounds (multiple targets) to take place.
- After awhile, the owl will spawn two pillars with 75 HP. Prioritise to destroy those two. After destroying both, the owl will be stunned for three rounds giving you the opportunity to unleash your attack power on him. This pattern repeats itself.

I entered the final fight (including the Final form scroll) with the following stats:
Health: 54
Attack: 57
Defense: 26
Speed: 34
Clarity: 24

Critical hit chance: 18%
Dodge chance: 22%
Stealh chance: 17%

Gear:
1. Double Candle
2. Hermit's Tiara
3. Bolster
4. Banishing Mace

In addition, you will also earn the following achievement:


Hope this helps anyone out there!

This achievement is comically easier than the other guides make it seem.

Simply play normally, grabbing as many items as you want.

Towards the end, pick up the spell scroll Transcendence.

I choose the Dark ending, as the boss is far simpler and does not use ranged attacks.

Simply save the scroll until you're about to defeat the boss, then use the scroll to remove all equipment. The achievement only cares about your number of items when you beat the run, so you'll get the achievement anyway.

I'd suggest using poison. Even just the poison spellbook alone works great to kill the boss after you're naked.

The spellbook will do 6 poison for a total of 21 damage. Even using the book after applying 2 poison before using the book ramps it up to 36 damage total.