You talk to the apprentice at the south end of the tower, then visit solberg in the hidden tower to get a crystal key. Then you find a hidden button in the east end of the tower gardens. It's pretty self explanatory from there.
I just killed Adze-Hakai and opened the box and got the crystalline plate and onyx scepter. However, when I look in my inventory, the only thing I see is the crystalline scepter. Am I doing something wrong?