Though iOS developer center has some documentations and snippets. But it isn’t sufficient information given to beginners. So, here I gather 2 more resources with useful articles.
Torque has make it into a better code library GameCenter.mm. It almost solves all my problems about Game Center. Meantime, please take note of the comments inside the articles to fix the issue appear on latest iOS 4.2.1 SDK. http://www.torquepowered.com/community/forums/viewthread/122529
About the Achievement, by default there is not pop up notification like ps3 and xbox to show you got the trophy. But thanks to Typenoeerror for sharing the code class over at http://www.typeoneerror.com/articles/post/game-center-achievement-notification.
I manage to join achievement notification into Torque’s GameCenter.mm and it works wonderfully.