How do you defeat the demon that amanda sends you in the mad snowny level...

Around the room are switches. You need to pull all the switches. When you have done this you will be able to use the metal gun thing in the middle of the room. Use the gun to hit the large metal ball things coming down from the roof. When this is done use your grapple on the sword piece. Level done.

For the second time:
Amanda uses the stone she found in Paraíso and morphs into the Unknown Entity itself. You have the Excalibur, so basically simply lock your aim on Amanda and keep swinging the sword. She moves really fast, but you'll still hit her nevertheless.

Don't stand still, as Amanda has a powerful attack which will drop you down and she might even get to chain a few combos dropping you off the arena. Keep running in circles and take cover behind the stones when needed. Also note the Excalibur's attack goes through walls, so never stop swinging it.

After a while, she will drop down and the interact symbol will appear on Amanda's head. Rush towards her and press the interact key to thrust Excalibur into her chest before she goes up. She'll recover her health and you have to repeat the whole process three other times