A Better Valiant - Hammerhead
First Available: Chapter 8
Other Requirements: Complete Living Off The Land & Obtain Valiant
Location: Hammerhead
Rewards: 800 EXP & Valiant II
You're able to accept this quest after obtaining the Valiant item which you get for trading Caem Carrots to Tony. In order to obtain these carrots you'll first need to complete the side quest Living off the Land during Chapter 8. Select the "weapons" option at Tony and you'll receive either the Plunderers, Force Stealer, Valiant or an Absorb Shield, which are all other items that you can upgrade at Cid.
To upgrade the Valiant weapon you'll need to collect an Earth Gemstone item which is found fairly commonly as a ground spawn in many different areas throughout the game. If you haven't been vendoring your treasures then you'll likely have one of these already.