Complete the objective to unlock the reward. Weapon Level 1 (Slot 1) is not missing, it comes pre-equipped on your character.

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