Do Riddler Trophies carry over into New Game Plus on Batman: Arkham City?

Solution 1:

Riddler trophies do carry over. According to the description of the "Perfect Knight - Day 2" achievement in the achievement guide at Xbox360Achievements.org:

To 100% the game you will need the following done:

• Complete the story on Normal or Hard AND New Game +
• Complete all side-missions on BOTH playthroughs
• Complete all riddler collectibles (data is shared on both save files)
• Complete all upgrades through leveling up and collecting (also shared)
• Complete all Riddler's Revenge challenges (as Batman)

I also believe that starting New Game+ does not prevent you from playing the first playthrough at the same time. I haven't done this yet, however given that there are two items in the menu (one or the normal game, another for New Game+) starting one doesn't stop the other.