Here is the full list of all 13 Nimble Fish achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Reach 300 points.
Buy whale
Buy all fishes in the game store
Buy Imperator fish
Collect 150 coins.
Reach 200 points.
Collect 75 coins.
Get into the mouth of a shark.
Fall on a flying bird.
Collect 25 coins.
Buy Goldy fish
Obtain a coin and die a second later.
Reach 100 points.