How many fragments do you need to get Fragment Skills?

Fragment skills are tied to specific milestones throughout the game: completing the main storyline, completing certain episodes, collecting a set of fragments that relate to each other, and so on.

These are the ones I've been able to find:

• Two you get right off the bat in Serendipity: Mog's Manifestation and Haggler
• Two you get for completing episode 5: Anti-grav Jump and Bargain Hunter
• One you get for completing the main storyline: Paradox scope
• One you get for getting all the fragments in the game: Clock Master

A guide by Krystal109 on GameFAQs lists the locations of all the rest, but if you happen to collect all 160 fragments, you'll wind up getting the vast majority of the skills.