Just as before, you will have to use the chair to get rid of the demons (screen). Be careful, though. Some of the monsters are capable of attacking you with their tongues and that will result in you losing your weapon. Also, remember that you'll have to find a new chair once this first one has sustained a lot of damage.
Once the battle has ended, take your time to explore your surroundings. First of all, you should be able to find a medical station here. Pick up some healing sprays if you have sustained even mild injuries. Once you're ready, proceed towards the stairs (screen), however the second you notice more monsters heading your way, go back to the ground floor and use a new chair to get rid of some additional demons.
You may proceed to the first floor without any other interruptions. Once you've arrived at your destination, go to your left and approach a new gate. Listen to what one of the guards has to say. If you've eliminated all creatures, he will allow you to enter this new section of the museum.
Keep heading towards your current destination, HOWEVER be careful here. Once again, you will have to deal with the black mass. You will be allowed to solve this problem using various approach methods. I assume that you don't have a burning chair at your disposal and that you're carrying only a few standard items. Start running and perform a jump towards the top right corner (screen).
Turn left and look up. Choose a pistol from your inventory and fire a single bullet at the lamp (screen). As a result, the lamp will begin swinging. Wait for the right moment to make a move and start moving forward. You can't leave the brighter area.
Eventually you will have to get to a second corner (screen). Sadly, you won't be allowed to exit the brighter area, because you would have been swallowed by the black mass almost immediately. Perform a jump towards that corner if you can't make it on foot.
Once you've reached a safe area, turn left and fire a second bullet at the lamp. Just as before, wait for the right moment to occur and start moving forward. This time it's going to get even tougher, because you will have to reach a small circle (screen) without being swallowed by the black mass.
Finally perform a jump towards a new corridor. It shouldn't be a problem, as long as you're careful. You may proceed to the next area of the map. Go to your left and approach a large panel (screen). Try placing your hand on the scanner, however obviously you don't have access to this part of the building. Move back a little and you'll be rewarded with a new cut-scene.
Wait for this conversation to end. One of the guards will unlock a passageway for you. Go there now and eventually you'll find an elevator. Enter the elevator and try using the panel. Press the middle button (screen), because we want go to down.
Sadly, the elevator is going to stop in a short while. You can't prevent this from happening. Don't worry, because you won't encounter any monsters right away. Approach the elevator door and press the action key (screen). Exit the elevator and go back to where you've talked to the security guard.