What you'll need to do:
Complete any level of the tower to have access to a terminal.
Collect all stars and then collect all sigils.
Access "Level 6" of the tower.
To access level 6 of the tower you will need to discover the password to unlock it using one of the terminals in the tower.
There are 3 fragments of the password in the Star levels of each area.
After you finish the 3 puzzles for the grey/silver sigils in the Star areas a piece of the password will unlock on a sign.
Area A will always have #**
Area B will always have *#*
Area C will always have **#
The numbers of the password change every time you save and quit so if you only collect 2 numbers of the password and quit the game you will need to collect the new numbers as they will have changed once you have resumed your save file.
Once you have a full password go to any available terminal and enter the password via the displayed prompts.