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