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.
Buy whale
Buy all fishes in the game store
Buy Imperator fish
Buy Goldy fish
Collect 150 coins.
Collect 75 coins.
Get into the mouth of a shark.
Reach 300 points.
Collect 25 coins.
Obtain a coin and die a second later.
Fall on a flying bird.
Reach 200 points.
Reach 100 points.