Here is the full list of all 36 Bunny Memory trophies - there are 24 bronze, 5 silver, 6 gold and 1 platinum.
I remember everything
Unlock 1 memory
Unlock 2 memories
Unlock 3 memories
Unlock 4 memories
Unlock 5 memories
Unlock 6 memories
Unlock 7 memories
Unlock 8 memories
Unlock 9 memories
Unlock 10 memories
Unlock 11 memories
Unlock 12 memories
Unlock 13 memories
Unlock 14 memories
Unlock 15 memories
Unlock 16 memories
Unlock 17 memories
Unlock 18 memories
Unlock 19 memories
Unlock 20 memories
Unlock 21 memories
Collect 10 Memory Points
Collect 50 Memory Points
Collect 100 Memory Points
Collect 50 mismatches
Collect 100 mismatches
Collect 150 mismatches
Finish the layout in 2 or less seconds
Complete each card type during one game session
Unlock secret memory
Complete layout 2x2
Complete layout 4x4
Complete layout 6x6
Complete layout 8x8
Complete layout 10x10