Bonus Challenge Levels appear only in the Collector's Edition of Royal Envoy 2, and can only be played after you have completed all 63 levels of the basic Adventure. Challenge Levels are not available in the Standard Edition of the game.
The Windows 8 "Special Edition" version of Royal Envoy 2 has additional bonus levels and achievements which are exclusively available only in Windows 8 version of the game. We don't cover those on this site.
You do NOT need to get 3 Stars on all Adventure levels in order to play the Challenge levels.(1)
Available Challenge Levels may be played in any order, unlike in Adventure mode where you must complete earlier levels before gaining access to later ones. However you have to gain stars to unlock them in Groups.
There are not any specific Achievements for completing Challenge Levels.(3)
And we KNOW about the bug in Challenge Level 25.
[November 23, 2011 Update: Playrix released a patched version of the game that fixes this bug "and other issues".]
Note 1: Be careful of confusing Challenge Levels with "Expert Mode". Expert Mode IS only available after getting 3 Stars on all Adventure levels and is intended to repeat all the Adventure levels with a timer that counts down even faster.
Note 2: Be certain that you are not playing the Adventure in Expert Mode when you select the Challenge Levels or you might find it impossible to finish the Challenges. It is not obvious that one affects the other until you try a Challenge Level and watch the timer plummet quickly. This may be an "unintended feature" (commonly known as a "bug") in the game. Playrix has yet to comment on this.
Note 3: However, you may replay Challenge Levels as often as you like in order to help you earn Achievements. (For example, Challenge 06 - Fisherman of the Year and Challenge 28 - Fishing Spots, if you are trying to earn "Arctic Angler Expert" Achievement for catching 250 Fish.)