I developed a strategy and used it to find all 441 fish!!!
Some hints that are not spoilers to how I did it.
In the beginning I found the fish from the common eggs that sold for the most money. I then bred those until I had finished all research. Then I found another fish that would sell for more and bred that until I had a good bank balance.
At this point, I found 4 fish from which I could breed all other fish. I had a plan and followed it. I used lots and lots of growth hormone (because I am a very impatient person) and in 2 days I bred all 441 fish.
Then I tested my strategy with another game and it worked a second time. Even better because my common egg high seller was more valuable in this game.
Sticking to the strategy that you come up with is very important.
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Sleep, who needs sleep, I have fish to raise.