Beautiful Butterfly :D:D:D
I would starch the background fabric pretty stiff, or use a stabilizer on the back. You can find wash away or tear away stabilizers, but I prefer to starch. I may still add some stabilizer behind where the body and antennae are sewn, as this is still just one layer of fabric.
Also, When going around the curves, stop with your needle down every few stitches, lift the presser foot, turn the fabric, if you try and keep going without doing this, you will get more puckers. It may take longer, but remember, it is still faster than sewing it by hand.
Fusible web will help a little with the puckers, but the main thing is to stop and reposition the fabric often.