Every time your hero gains a level, they also gain a point of Spell Mastery. Higher levels of Spell Mastery unlock a more powerful weapon of a matching color.
For example, if you want to unlock a Burning Scythe, you would need to earn both 40 in Fire (Red) and Magic (Purple) Masteries.
Purchase weapons from the shop
Some weapons are also available for Glory from the shop (tap select the 'Shop' icon in the bottom right-hand corner of the screen, then Glory Rewards). These weapons are related to the event at the time.
Missing a weapon?
If you have completed the maximum mastery level needed to unlock a weapon (e.g. 40 magic and 40 nature for Titania's Fan) but you still don't have the weapon unlocked, try levelling up. Levelling up will trigger the weapon to become unlocked in your game.