Gotham Knights contains only 3 Villain Cases (Side Quests / Side Cases). Completing all 3 Villain Cases unlocks the End of an Era trophy and achievement.
None of the Villain Cases are missable. You can still do all of them after the story in free-roam. They focus on specific villains: Harley Quinn, Mr. Freeze, Clayface. The one from Mr. Freeze is the longest, the one from Clayface is the shortest.
The cases from Harley Quinn and Mr. Freeze are available after finishing Main Case 01: Batman’s Last Case. Clayface’s case is triggered by defeating Clay Mimics at crimes in West End district, they spawn after Main Case 02: The Rabbit Hole. However, the later subcases are meant for level 20+, so if you are very underleveled the enemies can feel very tanky (even on the easiest difficulty). It’s better to do them after the story when you are sufficiently leveled.
Here are links to all 3 Villain Cases Walkthroughs:
For all Main Cases refer to Gotham Knights Walkthrough.
For everything else needed for 100% Completion, refer to Gotham Knights Wiki.