Take extra care on the requirements for the Moonflow Episode Complete. They are the strictest of them all.

Make sure you view the necessary CommSphere scenes to get the Besaid, Kilika, Mi'ihen and Bevelle Episode Completes.

Look up a guide on the Mi'ihen Mystery mission in Chapter 4. Best result is nabbing Rikku, if you can't do that, nab Chocobo Eater instead. DO NOT nab anyone else.

Don't forget to talk to Lian and Ayde in the Thunder Plains in Chapter 3. You need to do this for the Gagazet Episode Complete.

Do the PR mission during the first 3 chapters. It takes about 45 minutes dedicated time per chapter (for two chapters) to get it done.

Finally, have Zanarkand be your first stop in Chapter 5. It must not be your last.

...

Or, if you don't feel like doing any of that, just get to a high level and then fight in the Fiend Arena in Shinra's Creature Creator. If you unlock and beat the Youth League Tournament (7th cup) you'll be awarded one unique extra copy of the Mascot dressphere.

Whichever you prefer.