In order to acquire the elite gear, first renown with the Goons of Gotham needs to be achieved by doing the elite version of the Gotham City Zoo raid.
Cooperative (Renown): Elite Head and Elite Hands unlock
Friendly (Renown): Elite Shoulder and Elite Waist unlock
Favorable (Renown): Elite Legs and Elite Feet unlock
Trusted (Renown): Elite Chest and Elite Back unlock
The Riddler's overall color-scheme consists of three colors that can be chosen by the Player in the Style Window. Specific sections of the style's pieces can also be allocated a more specific colour by the Player.
Fit As A Fiddle, Right As A Riddle!: Collect all styles in the Riddler (Elite) set. Completing this feat will grant you a cost reduction on the elite Head, Shoulder, Legs, Hands, Feet, Back, and Waist items from the Gang War Equipment Supplier. (n/a Points)
Riddler On The Roof: Collect all styles in the Riddler set. Completing this feat will grant you a cost reduction on the Head, Shoulder, Legs, Hands, Feet, Back, and Waist items from the Gang War Equipment Supplier. (50 Points)
Regular and elite gear of the same style would usually differ minimally by the elite set having more glow, sparkle or otherwise enhanced features.