Ring of Pain

To get this achievement you must find the companion room and kill Sam. Sam is the big monster in here that will give you an item for killing all companions.

Sam is quite a tough guy to kill, but with just a few items you can kill him easily.

For this the key item is Hermit's Tiara.

Hermit's Tiara is a head piece that has a 100% chance to freeze the enemy as long as you have no more than 4 items. This is also a common item, so you can get it in the first floor. The first floor guarantees 2 loot drops, each drop shows 2 items + a free reroll on both. So that 8 chances in the first room to get it. If you dont, just restart the run. This usually takes me around 4 tries.

Once you get it, focus all of your upgrades into Speed. If you are faster than the enemy no other stat will matter as they will be frozen so you can just hit them until they die.

You will need to keep an eye out for a book or scroll that makes you immune to damage/take less on the next turn. Shield Up and Barrier are both great options. Again both of these are common so you have a good chance at finding one. I actually used the scroll Freeze but the other two are just as good.

When you have both Hermit's Tiara and either Shield Up or Barrier, you then need to find a companion room. This will be luck based. You will need to look for an exit with a frog over the top of it. Crossroad exits are useful to give you more chances at this.

When you finally find one, and you are equipped with Hermit's Tiara, and Shield Up/Barrier. You can kill Sam.

First activate Shield Up/Barrier. The hit Sam. You will survive his attack on you, and then youll leave him frozen. From here spam attack until he dies! For me the achievement didnt unlock until I left the room. Here is a video to show this.