Noctis’ starting weapon, Engine Blade, can be upgraded 3 times. The final time will change it to the Ultima weapon, but you need a Sturdy helixhorn to do so. This is not an easy item to find, unless you know where to look.
How to get the Helixhorn
There are enemies that can give you a helixhorn, and they are in a Hunt in Old Lestallum.
You cannot reach this location until chapter 6 or later. It is southwest of Lestallum on the map.
Just start your drive going west, and keep going south until you reach it. It is south of the parking spot at Tollhends Stronghold.
The Hunt with the enemies is called The Last Spiracorns.
This is a level 29 hunt that requires you to hunt 2 Duplicorns and 3 Spiracorns. You can repeat the hunt until you get the helixhorn, which are dropped from Duplicorns.
NOTE: You need Sturdy helixhorn and not the Crooked helixhorn.
Once you get the helixhorn, return to Cid to have him upgrade your weapon. Make sure you do not have the weapon equipped when you do so.
Also, be aware if you have quests to upgrade other weapons. You can only give Cid one item at a time, so if you have the required materials to upgrade other weapons, he might ask for those first.
If it asks you to turn in another material, the only way around this is to sell the material if you do not want to wait.
Some materials may be rare, so you might want to just turn them in and get the upgrade until it asks you to turn in the helixhorn. Just complete quests or hunts until they are ready.
You will have to wait while he upgrades, so complete other side quests or hunts until it tells you the weapon is ready.