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