Ascension Chamber/Meeting Room
Train a little to get use to Dante's style. In Meeting Room you'll meet a new, better version of Scarecrows. Go to Experimental Disposal.
Experiment Disposal/Security Corridor
Go down using elevator. Do you hear an alarm? Now you have 10 minutes to leave this place. Fall down and take Gold Orb. Activate the machine and go inside the elevator. Destroy Two Frosts using Rebellion style. On the top, break a Red Orb Statue. Just after entering the next room you will fall down. Take Key of Cronus and jump to the top using blades as stairs. Oh no - lasers again. Slow time and avoid them losing as little energy as possible.
In Grand Hall use Swordmaster style to defeat knights. You can go to Gauntlet room to destroy Combat Adjudicator or to leave the castle instantly.