Amethyst Bunny

Gem critters need an underground town. They appear only at cavern depth and only in range of housed NPCs, so the method is to build a village down there, stand in it, and wait. Rain lifts the odds noticeably, which makes a storm the right time to go sit in your cave town with a net out. Amethyst is at the common end of the gem rarity order, so it is usually the first one you meet.

It has almost nothing to it, so a wandering enemy can kill it before you get close and a stray shot of your own does the same. Swing the Bug Net early. Once caught it travels in your inventory and can be let go anywhere, or you can build the Amethyst Bunny Cage, which is a one-way trip. The bunny is furniture from then on unless you run the cage back through Shimmer. They also go into Rock Candy if you would rather eat one.

The eyes stay lit in the dark, which is how you spot one across an unlit cavern. A Party swaps most of them out for party-hat bunnies, so hunting during one is wasted time.