Instructions
Go to any save point and press "X" to access the menu. Choose "Upgrade" and then "Upgrade" again. Choose "Weapons." Choose the weapon you wish to level up.
Move the cursor to a component from the list available. Components are dropped by enemies, found in chests or purchased. Each component levels up the weapon by giving it so many Experience Points, or EXP. They also build up, or subtract, the bonus multiplier, which raises the amount of EXP the weapon receives.
Press "X" after choosing a component to see how much it will level up the weapon. Press "circle" if you do not want to use the selected component and choose another one. Press "X" to use the selected component. The EXP number on the left side of the screen will go up. When the EXP reaches a certain amount, the weapon will level up.
Level up the weapon as much as you can, until you run out of components, and then continue with the game. Level up the weapon again upon reaching another save point. Eventually, the weapon will reach max level and there will be a star next to its name.
Select the max level weapon in the "Upgrade" menu. Move the cursor to the special component needed to synthesis a new weapon, if you have acquired it. Press "X" to select the item. The weapon will become a new one, and its stats and level will change.
Repeat until the weapon is the highest level it can become, and synthesize a new one again. When a weapon can no longer be synthesized, it is called "Omega."