This is borderline story related achievement. Butterfly nests are spots where you can find butterflies (surprise!). They don't show up on the minimap but do on-screen, they appear as a bunch of blue butterflies flying around. All you need to do is walk into them and choose kill or take. Kill will allow you to kill it for experience, taking it exits the dungeon.
Your first chance to get this is during the Mausoleum of Metal, when you're visiting fort he second time. You'll have some tutorials with Kyo, and you'll go below ground, and then back up above ground. While following this path, you'll see a butterfly nest on the way. It's in the M.o.Metal N zone at the coordinates X12 Y18. This appears to be a 100% spawn when you're doing the story missions here. However, they spawn in just about every dungeon, so if you somehow miss it in the M of Metal, you can get it elsewhere.