This character story becomes available at the start of Chapter 2. Make sure you’re controlling a different character so you can talk to Natsu and start this CS.
[-] Go food shopping!
Fast-Travel to the Fountain Plaza and talk to the vendor to get some food. Just watch through the cutscene and the quest will be complete, raising Natsu’s max character rank will increase from 3 to 6.
This character story becomes available in Chapter 7, Episode 1.
[-] Find someone to take the egg
[-] Defeat the monsters on Hakobe Mountain
[-] Find out how the egg is doing.
First, head to the Kitchen and talk to Elfman. After that, travel to Hakobe Mountain then head west to find the marked flutterers. Defeat all of them in battle then travel back to your guild. Talk to Elfman or Lisanna to find out what happened to the egg. The character story will be completed shortly after, increasing Natsu’s max character rank from 6 to 9.
This character story becomes available in the Final Chapter.
[-] Teach the phony salamander a lesson!
Travel to Crocus and talk to the marked NPCs. Finally, travel to the Market area and talk to the generic dark guild character to trigger a battle. Defeat him easily then travel back to the guild to complete the quest. Natsu’s max character rank will be increased to 10.