Completing the hard story in Batman Arkham City isn't easy. You should start by familiarizing yourself with the layout of Arkham City. This will help you plan your routes during missions. During combat, keep an eye on the enemy's health bars and special abilities. Some enemies may be immune to certain attacks. In the exploration part, look for Riddler trophies and other collectibles as they can sometimes unlock useful upgrades or additional content. The story missions themselves are filled with challenges, so make sure to save your progress regularly.
I'm not sure which specific 'whole story' you're referring to in Batman Arkham City. There are multiple storylines in the game. The main one involves Batman being trapped in Arkham City, a large prison area in Gotham. He has to deal with various villains like the Joker, who has a devious plan as always. And there are side stories about other inmates and their motives too.
One key element is the setting of Arkham City itself. It's a dangerous place full of criminals. Another is the Joker's plan. His actions drive a lot of the story. Also, Batman's relationships with the other characters, like Catwoman, are important. She has her own motives and sometimes helps or hinders Batman.
One common theme is power struggle. The gangs in Arkham City are always vying for control, and in fanfics, this can be explored in depth. For example, how different leaders rise and fall.
The toughest challenges in the hard story include the boss battles. Some bosses have complex attack patterns and high health, like Mr. Freeze. You need to be very patient and observant to defeat them. Also, the stealth sections can be difficult, especially when there are a large number of enemies in a small area.
The story often involves Two - Face creating chaos in Arkham City. He sets up elaborate schemes that are based on his idea of 'justice' which is warped by his split personality. Batman has to figure out how to stop him without causing more harm to the already chaotic Arkham City. This includes tracking Two - Face down in his various hideouts and dealing with the traps and henchmen he has set up along the way. It also delves into the backstory of Two - Face, how he became the way he is, which gives more depth to his character and the overall story.