Bugs are everywhere Animal Crossing: New Horizons. Various species appear during each of the months, and some only appear at specific times, when you have particular items on your island. The peacock butterfly, for example, only appears on hybrid flowers. You have to create a hybrid flower if you want to catch it.
The first thing you need to create is a hybrid flower using whatever species you have. While many players report that they capture the Peacock Butterly through a hybrid creation, most note that it comes from specific colors, such as a purple, blue, and black flower. Each of the flowers requires different color combinations. For example, if you have purple roses, you should use a pair of white roses if you want purple tulips, you need two orange tulips, and if you want to have purple pansies, you need two hybrid red pansies for Do them. Roses or tulips are the easiest combinations, so try adding them to your island and having them readily available.
To make a hybrid flower, you need to place flowers next to each one and give them only one space. Now you need to water them daily, and eventually a hybrid will sprout. When your hybrid is ready, you should now adhere to the Peacock Butterfly pattern and routine. It only appears from March to June in the northern hemisphere and from September to December in the south from 4 a.m. to 00 p.m. You can probably find him landing on the hybrid you created. When you see it, slide over it and try to capture it. You can sell it for 19 bells to Tommy and Timmy in Nook's Cranny.
You can find a variety of various insects and fish, depending on the correct conditions. Be sure to study each part of your New Island Skylines to see if any new bugs appear and if you can catch new fish.