There are a total of 12 Predator Challenges in Batman Arkham Origins. Earning 3 medals in each of them is required for the "Medalist" trophy and achievement. These challenges automatically become available when playing through the story. To unlock the six extreme versions you need to beat campaign challenges.
Certain abilities and gadgets are needed for some of the medals, so it's highly recommended to complete the story first and buy all of Batman's upgrades.