You start with a single slot for Weapon Level 1 equipment, but you can gain access to additional weapon slots at increasing levels by meeting the requirements indicated below.

Weapon	How to unlock
Weapon Level 1 (Slot 2)	Beat The Fire Elemental in Vorios.
Weapon Level 1 (Slot 3)	Sink The Flagship in Palias Harbor.
Weapon Level 2 (Slot 1)	Defend The Well in Khorad Basin.
Weapon Level 2 (Slot 2)	Beat Sundrax in N'Aquali.
Weapon Level 2 (Slot 3)	Close The Portal in Alkazaba Mines.
Weapon Level 3 (Slot 1)	Befeat The Ice Elemental in Icecreek Sanctuary.
Weapon Level 3 (Slot 2)	Beat The Undead Brute in Braverock.
Weapon Level 3 (Slot 3)	Beat The Tallicus in Enigmar.
Weapon Level 4 (Slot 1)	Beat Zeptic in The Azabrak Ruins.
Weapon Level 4 (Slot 2)	Destroy The Dark Energy Cannon in Greyveil.
Weapon Level 4 (Slot 3)	Beat Zane in Ashgar.
Weapon Level 5 (Slot 1)	Beat Karr Tel in Ashgar on Deity difficulty.
Weapon Level 5 (Slot 2)	Beat Zeptic in Ashgar on Deity difficulty.
Weapon Level 5 (Slot 3)	Beat Sundrax in Ashgar on Deity difficulty.