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