After performing a Tier Up upgrade on a weapon you can use Weapon parts and Hunter bucks to purchase it. Or, if you’re in a hurry, use Gold to bypass all requirements.

Open Mystery Box ---> Get Weapon Parts --> Craft Weapon Upgrades

Post Tier Up, Crafting requires a certain amount of Parts and Hunter Bucks, can be bypassed using Gold. Weapon Parts can be found in the Hunter’s Crates.