Challenges appear in the top right corner of the screen at that the start of every hour and last for 20 minutes, you have to be mastery level 10 for these to appear.
These challenges require you to complete dungeons in specific biomes and have three tiers:
For the achievement you have to complete 10 of these challenges.
To get these points you need to complete dungeons in the biome that the challenge states, you get 1 point per dungeon but this is multiplied depending on the difficulty portal you compete the dungeon in and if you use the bonus classes specified.