There are 15 Trophies that can be collected.

BRONZE

Too Hot
10 flowers sunburnt

Irredeemable
100 flowers sunburnt

Cumulo Nimbus
1000 rain drops have fallen

Happy Noah
10000 rain drops have fallen

Sorcerer's apprentice
Storms raged 10 times

Zeus is angry !
Storm raged 1000 times

My first gift
One or more flowers have been sent to a friend for the first time

My first crossbreed
A new flower has been converted for the first time with Labee the bee

Full slots
Every slot on the screen is full

Pretty Bouquet
At least one flower from each species have been unlocked

Composition
At least three flowers from each species have been unlocked

Hanabi Festival
Every common flower has been unlocked

Connaisseur
All of the five legendary flowers have been unlocked

SILVER

Vivaldi
Level 5 reached: four seasons have passed by

GOLD

Unstoppable!
Level 57 reached: fourteen years have passed by

http://www.ps3trophies.org/game/sunflowers/trophies/