The Campaign Challenges function the same way as Batman's and you do have to complete all of them again as Robin, plus Black Mask Campaign. They are the same challenges that you've done before, so they shouldn't give you too much trouble. These are the modifiers that I used. You can make your own combinations if these aren't working for you, but they worked well for me. Remember, you only get three retries total, but you get unlimited retries on the first challenge room.
See Campaign Nightwing for the complete list of modifiers that I used. You can also use KingBroly's guide for the modifiers since they will work too. The modifiers that I used for Robin's campaign challenge is below. There are only two maps in this one, but you still get the full three retries.
Black Mask Campaign (Only needed for Robin)
Black Mask - One Hand Tied
Freight Train - Decreased Health, Gadget Malfunction, Super Powered
Note: The challenges that you have to do for the trophy are the same ones that you had to do as Batman, plus the Robin campaign. The following challenges DO NOT count for the trophy. Any medals that you get in them will not matter.