On the web version - you will see the Path Progression with all requirements on the "My Challenges" page.
When you point with your mouse on the lock screen, the requirements will be displayed, for example:
Achievements are only added to your account and path when a challenge ends.
This is because the achievement calculations require the final standings for both you and your photos.
So once a challenge ends you will see the change in the Achievement count both in your profile and your status.
Note:
1. You must complete all of the necessary achievements in order to progress to the next status.
2. You can't skip over a certain status even if you completed the requirements for the next one.