Here is the full list of all 10 Fish Catcher achievements.
In single mode, catch the first commonfish
In single mode, catch ten commonfish
In single mode, catch twenty commonfish
In single mode, catch the first goldenfish
In single mode, catch ten goldenfish
In single mode, catch twenty goldenfish
In a round game of single mode, the first fish you catch is a bombfish
In a round game of single mode, do not catch commonfish, catch three and more goldenfish and then end the game
In a round game of single mode, do not catch goldenfish, catch ten and more commonfish and then end the game
In a round game of single mode, do not stretch out the hand in the first 20 seconds