Instructions
Play the game until the season turns to Summer. This is the only time that the beetles will appear in the game.
Walk around your farm and look at the tree trunks and walls. You will notice that the beetles cling to some of these.
Press the "L" button until your character is in walk mode. If your character is in run mode, the beetles will be scared away when you try to approach them.
Slowly walk up to the beetle until you are standing about one square away from it and press the "A" button to jump, then the "B" button. This will allow you to capture the beetle without the use of a net.
Sometimes you may need to approach the beetle from the side instead of head-on in order to achieve success. Try different methods to see which works best for your situation. A lot of the beetles appear only at night like the one you'll find on the tree beneath the windmill.