Ring of Pain

I personally did this on double candle which I believe is unlocked after beating the game on candle at least once.

Double candle allows you to choose a starting item off the bat for your run. I chose Hermit's Tiara which makes your attacks freeze if you have 4 or fewer items equipped. I believe double candle itself counts as an item so therefore you are allowed to pick up 2 extra items throughout your run to floor 12.

Your main stat focus will be speed as if you can ensure you attack first, you can freeze spam every enemy, including the exploding ones which no longer explode due to being frozen which is great for this achievement. Don't put anything into defense and clarity from the stat pick ups, get speed and maybe also attack to keep up as you descend.

You'll need to get a lot of speed in order to be able to kill the Constrictor enemy if it spawns, as it has 'intimidate' as its effect so unless you attack first, you won't be able to kill it via attacks at all. Believe it has 15 speed.

The two items I personally chose to take were a Jewel necklace early which was 4 speed. And my second item was the spell Plague. This was very clutch in doing true damage when the freeze tactic wasn't viable against that enemy. Make use of the reroll as you'll need the 2 items you do take to be quite good for the build to make it.

Avoid the Reprieve event as I believe the Owl counts as an creature and you will not be able to kill it.

The Dark for Days event may also help but I didn't get it myself, this room lets you skip the next two rooms and adds 2 to the current number.

This only took me 2 attempts using Hermit's Tiara when going for this achievement, dying early in the first attempt and getting it with ease on my second.

Any feedback is greatly appreciated, hope this helps.