Can be started while another weapon skill quest is active
Walkthrough
Talk to Zalsuhm with your job specific Nyzul Weapon equipped for a cutscene. Note that only the base level weapon is required, no upgrades or progress along the An Imperial Heist quest is required.
Once you have acquired enough Weapon Skill points, you will instantly be able to use your new weapon skill, but on your Nyzul Weapon only. It will simply appear in your list of weapon skills without any message in the chat log.
Only your CURRENT number of floors completed counts. So for example if you received the weapon and started the quest with 90 floors completed, and then did a 91->96 run, you only need 500 WS points to unlock the Weapon Skill. If you already did 500 WS points with the weapon, you will get the WS when the progress is saved to your Runic Disc.
Return and trade your unlocked weapon to Zalsuhm to allow the use of your new weapon skill on any weapon (of the same type, on that job).
Prior to unlocking the weapon skill, returning to Zalsuhm and trading the weapon will provide a rough gauge on how far along you have progressed. As you get closer to unlocking the message, the message he gives you will progress.
I sense only a mote of energy present. You still have a long way to go.
I can feel a marked increase in energy compared to when I first held it. Keep up the good work.
The energy is threatening to burst forth. It won't be long now.
You've done it! Energy is overflowing as though the floodgates have burst open!
The fourth message only appears after the unlocking is complete, and is followed immediately by unlocking the weapon skill completely.
Client: Zalsuhm (Lower Jeuno) Summary: Self-styled leading researcher of mystical artifacts, Zalsuhm, claims that the weapon you acquired deep within Nyzul Isle conceals immense power. Wielding the now unlocked weapon will cause a magical evolution to take place...eventually.