This side quest can only be completed after you have found the White SeeD Ship in this section of the game:
Combat King 003, like the other magazines with similar names, teach Zell how to complete new Limit Break attacks. This one specifically is obtained through the ongoing side story between Zell and the so-called Pigtail Girl. Earlier in the game, she awarded your team with either a 
Remedy or a Mega Phoenix depending on whether or not you had Zell in your party.
Start off by going to the Library in Balamb Garden and making sure you already spoke to the Pigtail Girl. She should no longer be in the library, indicating that you already completed this step.
Fly the Mobile Balamb Garden back to Balamb Town and head inside, but make sure that you have Zell in your team before you head in to the actual town.
As you enter Balamb, a girl should walk by in the very first screen under the Gas Station sign (shown in the screenshot below).
Speak to the girl and she will mention to Zell that a girl with pigtails stopped by his house. Now head down to Zell’s house for a quick chat with his mom who will tell him that no such girl stopped by their house.
Go down to the Balamb Hotel and spend the 100 gil to stay the night. Zell will be gone when the other two party members wake up.
Head down stairs back into the lobby to find Zell and the Pigtail Girl having a conversation. The conversation is garbled but its pretty evident that the two are into one another. Either way, at the end of their conversation, the Pigtail Girl gives Zell a copy of Combat King 003, a very nice reward!
