Goldfish was a pain in the neck to catch and it’s not even listed as rare.

If you have Switch Online, find a free treasure island and fill your inventory with fish bait. Barring that, dig up a bunch of clams. The 3.0 update lets you craft 10 things at once now, so that makes grinding out fish bait honestly a lot faster. Then just throw bait and if the shadow isn’t the size you want (goldfish is small ~~but not tiny ~~IIRC), throw more bait to roll again. Know the times the goldfish can spawn (all day actually, and it’s 3/5 stars of rarity, and very small/tiny, just looked it up).

Also note that a treasure island with fish won’t contribute to your Critterpedia, but you can fill the museum with “found”/“gifted” fish, bugs, and sea creatures. (If you catch the fish there, it counts, but if you find it in a container on the island proper, it doesn’t. Though note most treasure island don’t have water.)