Challenges are daily missions that you can take on a couple times each depending on the mission. Sometimes they’ll have special requirements like the STR gear challenge which only lets you use characters with the attacker trait. These are pretty easy and drop a lot of useful items like training droids and rare equipment. Listed below are what challenges I have seen and when they have occured.
Str Gear Challenge – Attackers Only – Thursday, Saturday, Sunday, Monday
Agi Gear Challenge – Healers/Support Only – Friday, Saturday, Sunday
Bounty Hunter Challenge – Earn Mining Droids (Big Credits!) – Friday, Saturday, Sunday
Ability Mats Challenge – Earn items for special abilities – Saturday, Sunday
Int Gear Challenge – Tanks Only – Saturday, Sunday
Training Droid Challenge – Earn XP Quickly! – Saturday, Sunday, Monday