The first area you will enter is the outer cradle which at the start of the mission, has no enemies in it. The only NPC here at the moment is the ghost who is needed to finish the mission, the ghost is Lauryl who was murdered by the Grey Lady. After activating a gate you will be able to move into the inner cradle where the undead crazy patients are... unlike other undead in the game, the undead here have more strength and health than other undead, plus you may need confront undead face to face after breaking into their cells to get items on import, however this may only be if you lose the "Wax Musk" which allows you to enter the past of the cradle once you use it on the chair you take it from which is not anywhere near the cells.
After destroying all of the ghost's items, you will be able to escape after reading the incident report in the nursery tower, then you must kill yourself by jumping out of a window.