Do Xbox Live Indie games not have achievements?

Solution 1:

XBox Live Indie Games do not have achievements^{1, 2}. While Microsoft takes responsibility for reviewing and approving XBL Arcade titles, the review process for XBL Indie Games titles isn't controlled by Microsoft. Since they don't control the review process, they don't allow XBLIG games to have achievements that affect Gamerscore.

While Penny Arcade: On the Rain-Slick Precipice of Darkness episodes 1 and 2 were released as XBLA titles and therefore did have achievements, episode 3 was released as a XBLIG title and lacks achievements.

Solution 2:

There can be 'achievements' inside Indie games, however they do not increment / tie to your Xbox Live account, it'd be strictly tied to that Indie game. I would assume this is because there would be users with 500k+ achievement scores if the developers were allowed to put in achievements (Ex beating level 1 would give you 1000 points or something).