Hi, it's super flattering to hear from someone so long after putting the game out! To get through that door in the violet area, you need to activate the console in the room at the end of the red area where you and Emma fight the turret together. That will cycle the power and cause the doors to the secret, final area to open.
To kill Phaiston himself you need to go through a pretty convoluted path:
- cooperate with Emma in the red area to wire the core
- use the terminal to cycle the power in that room before you leave
- kill Emma immediately afterwards and take the detonator from her
- go back to the sealed door in the purple area, which will now be open
- in the area beyond, when you reach Paris, don't immediately murder him (this is possibly the most difficult step.) Disarm when he asks you to but keep the detonator equipped.
- join him on his escape pod
- during the ending sequence, Phaiston will now talk to the reporter from onboard the station instead of Paris. When he starts talking, press the button to activate the detonator.