This battle takes place in Lost Izalith, which is accessible from the Demon Ruins beyond Quelaag's Domain.
The Bed of Chaos is one of four primary bosses that you must defeat to open the path to the Kiln of the First Flame which leads to Gwyn, the game's final boss. You must first defeat the Ceaseless Discharge to drain the lava so you can access the bulk of the Demon Ruins.
This boss can be defeated with little trouble by using a built-in exploit. It will not become hostile to you until you attack it or until you run to the far end of the area and pick up the Gold Hemmed Black Set on a corpse. Once you do, it will wake up and rip its appendage off, which creates a lava explosion. Wait for this to happen before running as fast as you can back to the fog wall. The boss will follow you and eventually jump towards you and grab the nearby ledge. Simply attack his hand several times and he will fall to his death, resulting in a cutscene that makes the rest of the Demon Ruins accessible.
Lost Izalith can be accessed after defeating both the Demon Firesage and the Centipede Demon in the Demon Ruins OR by joining the Daughter of Chaos covenant and donating 30 Humanity to Quelaag's Sister, which allows you to open a shortcut door to the right of the Demon Firesage's fog wall. Either way you can progress through Lost Izalith to eventually find a fog wall that leads to the Bed of Chaos encounter.
This encounter is unique in that the boss is not a standard type enemy, but instead a large tree-like structure:
Your goal is to destroy the two nodes on the left and the right, which opens a path in the middle that leads through breakable branches to a small insect creature that can be killed with a single attack. The boss will be constantly attacking you with fire attacks and giant swinging branches as you try to move around the arena.
Should you die, you'll have to run pretty far to get back to this boss but if you manage destroy one or both of the side nodes, they stay destroyed so you aren't starting the entire battle over each time. One way to approach this boss is to run to either side and destroy the node, then save/quit, which starts you outside the fog door. Re-enter and destroy the opposite node, then save/quit again. Re-enter the fog doof and make a run down the center to get to the path with the small creature at the end.
An advanced technique (and the way I always do it) involves
running to the middle of the area and quickly throwing a firebomb at each node, lining up throws with precision by aiming with a bow. You can then immediately run forward through the central opening to kill the creature inside and avoid all the attacks from the large, main enemy. I had to practice several times (and you only get one try per playthrough) to get comfortable with it.
Start by having your bow equipped and firebombs ready to throw. After you slide down, run straight to the front of the area. Once you get there, press B to hop backwards into the starting position, illustrated
HERE. Aim your bow to the left side, putting your crosshair
HERE, then unaim and throw a firebomb. If done correctly, it will destroy the node and trigger a cutscene. Quickly aim your bow again and move it to the right side, putting your crosshair
HERE. Unaim and throw another firebomb, which should destroy the node and trigger another cutscene. Then simply run/roll forward through the path to the small creature inside.
Once you defeat Bed of Chaos, the achievement will unlock. Good luck!
As always, refer to
http://darksouls.wikidot.com for specific information relating to items or locations.