Upon reaching the Palace, you'll encounter Alfred Ashford. Your goal here is to gain access to his mansion. This involves solving several puzzles, including the 'Eagle Plate' puzzle and the 'Music Box' puzzle. Collect the various emblems and keys scattered throughout the Palace and its surrounding areas. Be wary of the Bandersnatches that patrol the hallways; they are fast and can deal significant damage. Conserve your handgun ammo for more critical threats.
