Those other methods include:
Randomly from Silver and Gold-haloed Sacks in Heaven-on-High Randomly from Fete Presents in the Ishgardian Firmament Randomly from Material Container 3.0, purchased for 20,000 Grand company Seals in either Ul’dah, Limsa Lominsa or New Gridania.
While all of these methods require a bit of luck, at least you’ve got options. Seeing as The Lost City of Amdapor (Hard) is a Level 60 Dungeon though, it may be your best shot. You can grab a couple friends and unsync the dungeon in under five minutes. Worse comes to worst, you can even try throwing up a PF for others in need of a bright butterfly.
Completing The Lost City of Amdapor (Hard)
Added in Patch 3.2, you’ll need to do just a few things to unlock this Dungeon. First and foremost you’ll need to have completed the Level 50 Main Story Quest “The Ultimate Weapon”. Then with that out of the way, seek out E-Sumi-Yan (Old Gridania – Stillglade Fane, X:6 Y:11). He’ll provide you with the Quest “One Night in Amdapor”. This Quest is simple enough: you just head to Camp Tranquil in the South Shroud. Chat with Raya-O-Senna, and then Alphene (South Shroud – Rootslake, X:14 Y:31). You’ll then be required to complete the Level 50 Dungeon The Lost City of Amdapor. Synced or unsynced, it doesn’t matter for the purposes of this particular Quest. Once that’s turned in, you can then pick up the next Quest from E-Yumi-San. The only requirement here is that you’re Level 60. “One More Night in Amdapor” sees you heading right back to Rootslake. Then once again chat with Alphene outside the Dungeon and you’ll have it unlocked. Now all that stands in the way of your Morpho Minion is some good old-fashioned RNG. Hopefully the Chest you come across after conquering Kuribu holds your butterfly. Best of luck with your catch, no net required.