The achievement is gained at the end of the Crimson Castle area. Throughout the course of this mission you will have to launch 3 catapults to try and drop the gate to the Crimson Castle. The first one has a few enemies between you and it but nothing major to worry about. Once you launch the catapult it will be obvious it doesn't do enough damage to drop the gate so you will have to find a second catapult. Here is the mini-boss fight for this area.
Evil Brick and Evil Mordechai
You can think of this fight like the fight with Smaug and Orenstein in the first Dark Souls. You will have Brick lumbering around the arena dealing heavy damage with his melee attacks and Mordechai warping around the top of the arena firing from long distance and sending birds at you. The arena is basically a circle with 3 embankments on either side. I kept myself hidden behind the embankments for the first part of the battle and dealt with Brick keeping my eye on the mini map to make sure Mordechai didn't have a clean shot at me. I would lure Brick around the back of the obstacles and unload with everything I had then as he moved closer dip out of cover, fire a few covering shots at Mordechai, and move to the other side of the arena and repeat until Brick fell. Once Brick is down pick a good medium to long range weapon and start chopping Mordechai down. I believe the birds he launches will bring you out of Fight for your Life mode but can't confirm as I've only played it once. Once both are in the ground the Mini-Boss fight is over.
The next move is to the second catapult. It will have a berserker attached to it which you will have to feed skag parts (located in an adjacent area) and dynamite (located in the same area as the catapult) before you launch. Once this is launched you move towards the third catapult. First you will shoot the moon out of the sky. Then you will have to retrieve the moon you shot down and load it into the catapult. The firing of the third catapult drops the gate to the Crimson Castle and you can move into the final area of the mission. Once you negotiate the castle itself it's time for the boss fight.
Lillith has two primary attacks in the beginning. I stayed close to the middle of the map so she always warped dead center and does a slam attack which produces an energy wave close to her and fires projectiles from her. She can be unloaded on once she hits for several seconds before she begins her second attack which is straight dives across the arena. The first dive will always be directly at where your character is standing. Once you see her get ready to move get out of the way as quick as possible and the next several charges are far easier to avoid. Then she will repeat the pattern until she hits 50% health and you move to phase two. In phase two of the fight her warp/slam attack will become much stronger as will the projectiles fired from it. At this point she also in my game began warping and slamming at the top of the map and I suspect she can do it at the bottom of the map depending on your position. She will also summon 4 orbs in a square formation around the arena which will damage you as well. The good news here is the orbs can be killed dropping ammo/health and can be used to bring you out of Fight for your Life mode. Keep chopping and she will fall like everything else. Once Evil Lillith is defeated the achievement pops and you will be able to travel back to the PsychoScape to complete the mission. Happy Gaming ;)