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.
156/157 games completed (including DLC)
Completion percentage: 99.37
Latest retail completion: Army of Two: The Devil's Cartel
Latest arcade completion: Dust: An Elysian Tail
Currently Ranked #1 on Achievement Completion Percentage Leaderboard on TA