I notice there are bunch medals appears in Decorations section in TGM3... I just don't understand what are those medals are for and how do you get them...or how the heck the game works to reward you with those medals.
Indeed the TGM3 wiki page has no info on that. I think it's basically the same as TGM2s system (which you can read about here). Maybe someone else can tell us how they differ.
Medals and decorations are two different things. Decorations are mentioned in the "TGM3 document": http://mufunyo.net/tetris/tgm03.htm