The Polyjuice Plot is a quest that can be started by obtaining Polyjuice Potion from Professor Fig. First, head to "Professor Fig's Classroom" in the Astronomy Tower and transform into the appearance of the Headmaster during the event. Then, proceed on foot to the Large Hall.
Answer the Questions Flexibly
Professor Sharp, Madam Pomfrey, and Professor Weasley will start conversation events on your way to the large hall. You may answer the questions any way you want since they'll suspect you either way. It does not affect quest completion or story branches as well.
Once you arrive at the Large Hall, talk to the house-elf Scrope and obtain the password for the room. The correct answer to the question is "Pure-blood, forever," but even if you choose the wrong answer, you can immediately choose again without any disadvantages.
Hide Behind the Partition on the Upper Floor
After finishing the conversation with Scrope, your Polyjuice Potion will slowly lose effect. Hide yourself by heading to the upper floor of the Large Hall. Go up the staircase located in the northwest of the large hall and hide behind the partition at the back of the room to complete the quest.