Drops from the end-leveling content for Superman Mentored characters, specifically the Hall of Doom instance - Hero Side. Don't know about Villain side... Maybe try the Treasure Chest for the Joker's Funhouse where you fight Robin; the Level 11 shoulders are in that chest on Hero side for the low level mission, but it's a rare drop.
The DCUO-DB shows the Level 11 New Genesis shoulders dropping from the Treasure Chests in Joker's Funhouse and the Metro Station.
Wanted to revive this thread to find query on these shoulders, as of this post I'm trying to search for them in the Joker Funhouse. I thought this style could be purchased via Replay Badge?
what level are you? because you get the New Gensis style gear granted at level 30, don't you? it's been a while since I run any of that stuff, but I'm sure I remember you get them free from your mentor when you join the JLA. &, yeah, absolutely you can unlock them with replay badges.
Two ways to get the New Genesis Shoulders, complete the main story (you get a full set of New Genesis gear) or re-run the Supergirl/ Dr. Psycho Level 11 boss mission at the Metropolis General Hospital in Little Bohemia (the New Genesis Chest, Shoulders and Belt are Boss rewards).