Once you purchase a kingdom and finish the main quest there you will have access to the challenges. There are 10 tiers of challenges with 7 challenges in each tier. Each tier of challenges will have a different type of reward such as glory, gold, keys, etc. which you will earn a small sum of for completing an individual challenge and then a larger sum when you complete the entire tier of challenges.
So for this achievement you need to do 7 battles each in tiers 1-5 for a total of 35 battles. If you had all challenges complete prior to this update you will be starting on tier 2 so you have to finish 7 battles each in tiers 2-5 for a total of 28 battles.
Thanks to RadicalSniper99 for mentioning this, if you completed this before the achievements were live, you should be able to go into the challenges for that kingdom and have the achievement pop for you.