I completed a quest, but the quest list is not showing that I completed it. Why is that?

Quests will only show as completed once you meet the clear conditions after the quest becomes available.
For example, you may have cleared Chapter 1: Part 5 on Hard mode. Later, a quest is available for clearing Chapter 1: Part 5 on Hard mode. You will need to clear Chapter 1: Part 5 on Hard mode again to complete the quest.