Quaff a see invis vial and find the sneaky Alfar spy just outside the walls of the city of Utgard.
Ask spy help. He will ask you to incapacitate the two-headed ettin (killing him does not work).
Go to the Brokk, the brewer in the city of Joruvellir, and buy a pint.
Go back to the city of Utgard and find the two-headed ettin.
Give pint two-headed. He will drink the pint and the spy will sneak past.
Go north east south to the next room the spy is waiting in. Ask spy help.
He will ask you to move the statue in the king's chambers. Go east.
Push statue until it gives you the message that it moves a couple feet from the wall.
Go west and ask spy help. He will tell you how to use the healing mirror (nw2s from this room).