These are just the combos that worked for me, I'm not sure if there's more to it than that. I recommend growing the fish up to the orange or blue stage (whichever you want to work on) then manually saving the game. That way, if you make a mistake when caring for it, or if the RNG for the sick days/tank cleaning don't line up as you need, you can just exit to title and reload instead of having to wait for the fish to die.
Hope this helps:)