The list appears as follows. Note: All Challenges can be completed in Matchmaking, Custom Matches, or a combination of both modes. Use the "Statistics" view to see where you are for all of these not the "Leaderboards".

1 Life: 10 Kills - 1 Weapon
1 Life: 25 Bonus XP
1 Life: 5 XP - 5 Backpacks
1 Life: 50 XP
1 Life: Kill - 5 Weapons
1 Life: 15 Bonuses (different types not fifteen of the same one)
10 Kills - Every Weapon
10 Wins - Every Game Type
100 Wins
100 XP - Every Backpack
100 XP - Every Weapon
1000 Kills - 1 Weapon
5000 XP - 1 Backpack
5000 XP - 1 Weapon
500 XP - 1 Bonus XP Event
5 XP - Every Bonus XP Event