Don't enter the western hallways past the death chalice at this state. A ghost will come at you from the bathroom.

Take up position here. Open the door to any of the central library rooms and fight it out with all the enemies within them. Find health chalices in the rooms after the battle has ended.

Defeat the armour hiding between these book shelves. Take the axe, and the bronze key.

Finish off the ghosts in the washing room for some additional health.

Now enter the western hallways past the death chalice. Finish with the guards, the sub mutant, and the ghost in the bathroom.

Break the mirror in the bathroom and open the secret door. Find a 1-up. You may want to save it for later.

Continue.