Here is the full list of all 23 Sea of Solitude trophies - there are 6 bronze, 9 silver, 7 gold and 1 platinum.
Made it through school
Eaten by Whale 20 times
Got grabbed by waterhands 10 times
Opened a path through water
Shooed your first Seagull
Collected your first Message in a bottle
Connect with mirror Kay for the first time
Fired 30 flares
Fired the first flare
You have collected all of the other trophies.
Collected all bottles
Shooed all Seagulls
Respawned on couch in Skyscraper
Jumped headfirst into the water from a high point
Swam a very long distance
Travelled very far by foot
Travelled a long distance by boat
Swam long distance while whale was around
Finished Level 1
Reached top of the Skyscraper
Finished Level 2
Finished Level 3
Finished the game