Ring of Pain

There are a few different ways to achieve this task.
+Splash damage
+Soul damage
+Poison
+Detonate Spell
+Soul Spill Spell with a very large number of souls

This must be done in a single turn, though it can be either yours or the enemy's turn. If it switches to the next turn without them all dying it will not unlock.

The easiest way is to get the Volcanic Stone item which adds 1-3 explosive enemies on each floor, and pick up a detonate spell. Then simply find a path where 5 or more are on the ring and activate the detonate spell. (I'd recommend also having the Chestplate armor for reduced explosive damage, just in case you need to blow one or two up on yourself.)

If you can't find the volcanic stone, watch for the Visionary stone instead. This item reveals all cards on the floor so you can easily see if there are at least 5 to use a spell or try to cause a chain reaction with damage.
The Paths Volatile or Embracing Chaos work well for this if you don't have the volcanic stone.