Here is the full list of all 22 Sea of Solitude achievements.
Collected your first Message in a bottle
Collected all bottles
Shooed your first Seagull
Shooed all Seagulls
Fired the first flare
Connect with mirror Kay for the first time
Respawned on couch in Skyscraper
Got grabbed by waterhands 10 times
Jumped headfirst into the water from a high point
Fired 30 flares
Eaten by Whale 20 times
Swam a very long distance
Travelled very far by foot
Travelled a long distance by boat
Swam a long distance while Whale was around
Made it through school
Opened a path through water
Finished Level 1
Reached top of the Skyscraper
Finished Level 2
Finished Level 3
Finished the game