Exploring the castle isn't all that difficult. There is no one left aside from a few Calamity Monsters, that can either be attack or avoided. No, the real difficulty is getting the exploration done within less than two hours before Bahamut destroys the castle... And not alerting the wrong kind of person.

Upon reaching the pathway leading toward the empress's personal quarter, they'll be faced with closed lock. The door looks sturdy but it can definitely be blown off, if so needed.