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 a level with 5 enemies alive
Complete Time Trial mode with all the stars in all the levels
Complete all chapters in Time Trial mode
Complete a level in Time Trial mode
Complete a Time Trial level with only 1 second left
Complete all chapters in Normal mode
Complete Normal mode with all the stars in all the levels
Finish a level with 2 crabs still alive
Complete the fourth chapter: Arctic fire
Kill an enemy while he's inside an ice block
Complete the third chapter: Underwater volcano
Complete the second chapter: Reef ahead
Complete the first chapter: Shallow waters
Kill an enemy
Complete a level in Normal mode
Obtain 3 stars in a level
Finish a level losing no lives
Obtain a powerup