Here is the full list of all 16 Sym achievements.
Finish the tutorial
Finish all the "My own little world" levels
Finish all the "I want to disappear" levels
Finish all the "Fear and loneliness" levels
Finish all the "Build self confidence" levels
Finish all the "Rehabilitation" levels
Finish the game with Ammiel
Finish the game with Caleb
Make and share a level
Finish a user made level
Finish 100 user made levels
"Time… to die…"
Understanding binary mathematics
Climb and fall, climb and fall, climb and fall...
Complete the game with nine or less deaths
"Shut down all the garbage mashers on the detention level!"