I've been hunting golden animals, and just got my final one. I don't have spares at the moment, but for the grasshopper, I think you can cheese it with the following strategy:
Get a flare gun and flower boots. Stand on two squares of grass and shoot the flare gun into the space between those blocks; a single flare will last for a very long time. The flare will destroy any grass that grows on those two blocks; the boots will regrow the grass instantly. Stand there and swing your net on repeat. This can be farmed AFK by just finding something to hold down your mouse.