I'm almost positive that Batman's upgrades carries over to Nightwing and Robin. For example, the upgrade for Batman which allows him to remain hidden on a gargoyle even if a thug is scanning it with a thermal scanner. It applies to Nightwing and Robin as well.
I'm presuming that if you don't have that upgrade for Batman, then you won't have it with Nightwing/Robin/Catwoman.
136/137 games completed (including DLC)
Completion percentage: 99.15%
Latest retail completion: Saints Row IV
Latest arcade completion: Warface