The Oubliette is a secret area only accessible on the first floor of the Gungeon. Somewhere on this floor there is a lit fireplace, and you need to extinguish the fire to access a hidden switch which will reveal a secret room on the map. YOU NEED TWO KEYS TO ENTER THE OUBLIETTE, so plan accordingly!
There are three ways that I know of that can extinguish the fire:
1) Using a water or ice gun (such as the Glacier or the Mermaid shotgun). This is very RNG based off of luck from chests.
2) Rolling a water barrel into the fire. This is the easiest way to extinguish the fire. Somewhere on the floor there will be a blue barrel that allows you to roll it all the way to the room with the fireplace. This can be a bit tricky bit I've gotten the barrel to spawn 1-2 rooms away from the fireplace and even once in the same room. Make sure you do this when all enemies are killed so they don't accidentally shoot it!
3) Those red blob enemies that hop around leave a red gooey trail, and that can extinguish the fire, as well. This only applies if they spawn in the fireplace room, of course.
Once you pull the switch, check your map and you'll see that a secret room opened up. Head there and make sure to have two keys. Once you open the locks on the trapdoor and enter, your achievement will unlock.