Here is the full list of all 37 Song of Memories trophies - there are 23 bronze, 9 silver, 4 gold and 1 platinum.
Kanon moves in
First battle
Get Dream Unit
Natsume Kurihara appears
The game's opening plays again
Reunion with Kanon Hiiragi
Fuuka Kamishiro appears
Yuno Wakatsuki appears
Satsuki Tsushima appears
Makoto Asukaya appears
Collect every trophy
Complete every chart
Complete every illustration
See every sequel
Clear every end
Pass every "Around."
Kanon Hiiragi True End Clear
Fuuka Kamishiro True End Clear
Akira Tabunoki True End Clear
Yuno Wakatsuki True End Clear
Satsuki True End Clear
Natsume True End Clear
Kanon Hiiragi Normal End Clear
Fuuka Normal End Clear
Akira Normal End Clear
Yuno Normal End Clear
Satsuki Normal End Clear
Natsume Normal End Clear
Collect every Dream 4 You song
All Dream 4 You levels are highest
Get every Bad End
We all went to the pool.
Akira Tabunoki appears
Get all the normal Ends
Get Makoto's End.
The whole Kamishiro family is killed
The Dream 4 You opening plays again