There is no way to get an achievement completed percentage.

[haikami]

I am supposing that this is actually possible..
I tried with the gamecenter manager, but there's no method to do such thing,
I also tried doing:

        GKAchievement achievement = new GKAchievement(achievementId);
        percentage+=achievement.getPercentComplete();

But this method always returns 0.

[dejvid]

I think you have to get achievements with GameCenterManager in GameCenterListener callback method achievementsLoadCompleted. You are just creating new achievement. Your instance of achievement does'n know about state stored in game center.