From Halopedia, the Halo wiki
Challenges in Halo: Reach are daily and weekly objectives for posted in-game, on Halo Waypoint, and until March 31, 2012, on Bungie.net. Players can only view and complete challenges while connected to Xbox LIVE. All challenges are reset at 11am GMT (3am PDT) with Daily Challenges resetting each day and Weekly Challenges resetting each Monday. A player is awarded a certain number of Credits after completing an objective. Challenges cannot be completed on the Easy difficulty.
Players who complete a Weekly challenge are awarded the achievement "One Down, 51 to Go". Players who complete all of the Daily Challenges on a single day are awarded the achievement "A New Challenger".
A new feature, Custom Challenges, was added through Halo Waypoint as of November 2011. Users can make a challenge and invite friends to complete it as well as themselves. They can only be created in the official Halo Waypoint webpage, or through the Waypoint mobile app, but current invitations and challenges can be viewed in Halo Waypoint for Xbox 360. In June 2014, 343 Industries announced that Custom Challenges would be discontinued by September, 2014.
Custom Challenges have the following elements:
Up to five challenges may be created at the same time, until either the time ends or if the player succeeds in completing it, and "turns in" the challenge, freeing one slot for creation of a different challenge, however, credits will only be awarded once the time runs out. Once a challenge is made with a specific goal, such as headshots, that goal cannot be set for any other challenges of the same type until the challenge ends, in one way or another. If the player that created a challenge wants to cancel it, there is an option of forfeiting the challenge, which won't give any credits. The number of credits earned for completing each challenge depends on its goal, type and time, multiplayer matchmaking challenges seem to award the highest amount of credits, more specifically, headshots and wins challenges. For example, 300 kills in 60 hours will give 6389 Cr, 300 headshots in 60 hours will give 12282 Cr, and 75 wins in 48 hours will give 15825 Cr.
Strategies for common Challenges
Note: All Campaign challenges, unless otherwise labeled, must be done on Normal difficulty or harder.