Whenever you load up a game of Cosmos Invictus you’ll see a list of Challenges that are available to you:

There are always three challenges available at any one time. Completing one of the challenges nets you the reward indicated, so long as you complete it before the next batch of Challenges is introduced. To see when the Challenges will refresh just take a look at the timer at the bottom of the Challenges screen.

You can access the Challenges list to see your progress at any time by selecting it from the main screen.

The Challenges refresh every 24hrs (UTC time).

daily challenges view

Once you satisfy the Challenge requirements, after battle you will see a notification about the completion of the task and the relevant reward(s).

challenge completed view