As of the Babylon update, new challenges are available from Wallenstein's Special Contract Missions. Defeating them will (temporarily) unlock special rewards from the Exchange Broker. However, I believe you can only choose 1 reward at a time (or so Google Translate tells me). Cheers, great gladitorial fighting to you.
Emerging Pirates
HP: 1600 (Water), 2200 (Air), 2400 (Fire), 3600 (Earth)
Note: Uses Attribute element tech (all 4 elements)
Reward(s):
x5
Catalyst of Water (300 Roman Coins)
x5
Catalyst of Air (300 Roman Coins)
x5
Catalyst of Earth (300 Roman Coins)
Gluttonous Cook
HP: 10,000
Note: Uses Attribute element tech (Earth) +
International Chef items
Reward(s):
Meat Cooking Award x10 (90 Roman Coins)
Precious Food Award x5 (900 Roman Coins)
Nickname Issuing Documents (No.5) x1 (500 Roman Coins)
Transformed Crossbow Refitting Technique (1,500 Roman Coins)
Inferno Walter
HP: 30,000
Note: Uses Attribute element tech (Fire) + Trap Adventure-type techs
Nickname Issuing Documents (No.5) x1 (500 Roman Coins)
Luxury Flax Yarn x1 (1,500 Roman Coins)
Whirlwind Olaf
HP: 25,000
Note: Uses Attribute element tech user (Wind)
Reward(s):
Nickname Issuing Documents (No.5) x1 (500 Roman Coins)
Northern Scholar's Tool Box x1 (1,500 Roman Coins)
Correction: the Gluttonous Cook is Attribute element (Water). Apologies for the misprint.