Here is the full list of all 18 Lightfish achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Complete Normal mode with all the stars in all the levels
Complete all chapters in Normal mode
Kill an enemy while he's inside an ice block
Complete the fourth chapter: Arctic fire
Complete the third chapter: Underwater volcano
Complete the second chapter: Reef ahead
Complete the first chapter: Shallow waters
Complete Time Trial mode with all the stars in all the levels
Complete all chapters in Time Trial mode
Finish a level with 2 crabs still alive
Complete a level with 5 enemies alive
Complete a Time Trial level with only 1 second left
Complete a level in Time Trial mode
Complete a level in Normal mode
Obtain 3 stars in a level
Finish a level losing no lives
Obtain a powerup
Kill an enemy