There are 15 challenges found in the game. You can get 14 of them in one playthrough. Play the game picking all Brotherhood based choices.
Brotherhood Includes: Magneto, Mystique, Quicksilver, Juggernaut, Pyro, and Toad.
You will have all but 1 challenge in the game as long as you found all of the hidden ones in the levels. To get the locations for those, refer to this guide HERE. The challenges are all extremely easy and you should be able to complete most of them in one try. You can always replay them by choosing load and then selecting challenge. The key to getting the last one is to reload Mission 5: Uncovered. Make sure you have Nightcrawler teleport you to Cyclops. Now, load up Mission 6: Priorities. You just have to get to Northstar and talk to him. Because of choosing to teleport to Cyclops, he will now let you do his mission.
Note: Challenges are the perfect way to get your kill based achievements.