I remember being able to upgrade my weapon in the single-player mode Octo Valley using the eggs that you find in the levels. But after playing a couple levels and gathering a few hundred eggs, I don’t see any way of spending them. The pause menu doesn’t have an upgrade tab and the only NPC in the overworld is Marie who just has random things to say.
How do I upgrade my weapon?
After you beat the first boss in Splatoon 2 you should receive a message from Marie and Sheldon that will unlock the ability to upgrade your weapons and gear which is near the start of the first area in Octo Valley. Once you unlock the weapon modification station you are able to use your sardinium and eggs you find during the single player levels to upgrade your gear.
Source : Link , Question Author : Chase Sandmann , Answer Author : CyberSkull