The Challenges are similar in premise to Arcade League. In the original TimeSplitters's Challenge Mode, there are both unique challenges and missions that can be recreated in Arcade Custom.
In TimeSplitters 2 and TimeSplitters Future Perfect Challenge scenarios cannot be easily replicated due to increased complexity.
Most of the challenges have a mini-game feel to them and the objectives are often more absurd than those in the League. Completing challenges unlocks characters and other awards for Arcade Custom.