Their relationship could develop through mutual respect. Batman respects Supergirl's power, and Supergirl respects Batman's intelligence and strategic skills. They start by working on small missions together and gradually build trust.
One idea could be that Batman tries to train Supergirl to better control her powers in the context of the Injustice 2 universe. He might see her as a potential force for good against the tyrannical regime. Another could be that Supergirl discovers a way to bring back the more heroic Superman she once knew, and Batman has to decide whether to trust her plan or not.
Supergirl's exuberance and her willingness to trust can sometimes clash with Batman's more cynical view. However, in the context of a romance in fanfiction, this can be a source of growth for both of them. Batman might start to trust more because of Supergirl, and Supergirl might become more cautious under Batman's influence. Their personalities also play a role in how they show affection. Batman might be more reserved in his displays, while Supergirl could be more open and affectionate, which could lead to some sweet and sometimes awkward moments as they navigate their relationship.
In the Injustice 2 Batman ending story, Batman manages to defeat Superman. He restores order to a world that has been torn apart by the chaos of the Injustice regime. With Superman out of the way, Batman is able to start rebuilding society, bringing back justice and the rule of law. He also has to deal with the remaining super - villains and ensure that they are locked away safely.
Nightwing is a great choice. He has a strong connection to Batman as his former sidekick. In an Injustice fanfiction, Nightwing could be the voice of reason when Batman starts to go too far in his fight against Superman. Their relationship, with all its history and baggage, can add a lot of depth to the story.
Supergirl has super strength which allows her to lift extremely heavy objects. She also has heat vision that can be used as a weapon. And of course, she can fly. Wonder Woman, on the other hand, has super strength as well, but she has unique weapons like the Lasso of Truth which can force people to tell the truth, and her indestructible bracelets which can deflect bullets.
Alfred should be included. He can provide Batman with support and advice, and his unique perspective on things could add an interesting element when Supergirl is around. He might even offer her some tea and wise words.
A really cool story could be set in an alternate universe where Supergirl and Batman are the last two heroes left. They have to rely on each other completely and in the process, they discover new aspects of their powers and themselves. Their relationship could evolve from just being allies to something more complex and deep, with Supergirl teaching Batman to have more faith and Batman teaching Supergirl more about strategy.