Wiggle will want you to catch a Green Grapeskeeto for her in Bugsnax. The first thing you will need to do is actually find them. The Green Grapeskeeto will only appear in Simmering Springs, down on the beach, between 4:00 PM and 4:00 AM.
Catching them can also be a little awkward, as you cannot just catch them in a trap. If you scan a Green Grapeskeeto you will see that they love chocolate, and the description says that they slow down if they eat another Bugsnak.
This is exactly what you will need to do if you want to catch one. If you go to the small wooden ramp that leads down to the beach at the right time, you should see two Green Grapeskeetos flying around. Take out your Sauce Slinger, and fire some chocolate at one of them. The other one will rush in and start to eat it, eventually growing quite fat and finding it difficult to fly.
When it drops to the ground, run up to it and hit Square to catch it in a net before the timer runs out to catch it. None of the other Bugsnack should interfere with this. Some of them like chocolate, but there are no aggressive Bugnsax on this part of the beach that will knock you very far away from your target.
Now, you can give the Green Grapeskeeto to Wiggle and move on to the next part of the missions for her.