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