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