Here is the full list of all 13 Silver Star Chess trophies - there are 11 bronze, 1 silver and 1 gold.
Proof that promotion for the first time.
Proof that an passant for the first time.
Proof that castling for the first time.
Proof that lost match for the first time.
Proof that drawn match for the first time.
Proof that beat level 1
Proof that beat level 2
Proof that beat level 3
Proof that beat level 4
Proof that beat level 5
Proof that beat level 6
Proof that beat level 7
Proof that beat all levels without using “Undo” and “Help”