Instructions
Upgrade your farm. Speak with the Pokke Farm caretaker just outside of the farm in Pokke Village to purchase upgrades from him using your Pokke points. Get these points by completing Training School missions and finding Account items while on quests.
Upgrade the Insect Thicket and Bug Tree areas on your Pokke Farm to their maximum levels. You must purchase all upgrades in sequential order -- you can't go from Insect Thicket +1 to +4 without buying +2 and +3 first.
Gather insects from your Insect Thicket and Bug Tree once you have purchased the upgrades; Phantom Butterflies are rare, but you have the best chance of finding them with full upgrades.
Do high-level missions such as the Diablos, Tigrex, Kirin and Gravios quests. Expand Pickaxes are occasionally given as rewards during these missions and you can use these on any Phantom Butterflies or other components you already have in stock to gain an additional one.