You can only complete this side quest after you have found the White SeeD Ship in this section of the game:

Combat King 003, like the other magazines with similar names, teaches 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 you had Zell in your party.

Start by visiting the Library in Balamb Garden to ensure you have spoken to the Pigtail Girl at least once. 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 you have Zell on your team before entering the actual town.

As you enter Balamb, a girl should walk by on 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 100 gil to stay the night. Zell will be gone when the other two party members wake up.

Head downstairs back into the lobby to find Zell and the Pigtail Girl having a conversation. The conversation you overhear is garbled, but it’s 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!