There are 13 Trophies that can be collected.

BRONZE

the IDEAL
Clear Spring Valley in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

the POSSIBILITY
Clear Mystic Forest in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

the CONFUSION
Clear Soft Museum in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

the AFFECTION
Clear Splash Garden in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

the CONSCIOUSNESS
Clear Frozen Bell in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

the REVIVAL
Clear Stick Canyon in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

DREAMY !!!
Show your supreme skill by achieving the highest Acrobat Time rating, "DREAMY".

Mystic Garage
Try to guide the lost car in the Mystic Forest to the garage.

Merry Christmas!
Clear Spring Valley (Christmas).

SILVER

the GROWTH
Clear Twin Seeds in either BRAND NEW DREAMS or SEGA SATURN DREAMS.

into dreams…
Clear all stages with a score of Rank A.

Hello Mepian
Make a Nightopian and a Nightmaren have a hybrid offspring.

GOLD

Paraloop Master
Try to Paraloop all of Gillwing’s tail in one hit.

http://www.ps3trophies.com/forums/playstation-trophy-news/22717-nights-into-dreams-trophy-list.html