Here is the full list of all 15 Summer Pockets achievements.
Use the Character Gallery
Complete all scenarios
Complete the ALKA scenario
Complete Tsumugi's scenario
Complete Kamome's scenario
Participate in Islamon Battles
Complete Ao's scenario
Use the Music Gallery
Use the CG Gallery
Complete Shiroha's scenario
Complete the prologue
Play table tennis with Tenzen
Complete the Islamon Battles
Collect all four Celestial Beasts Islamon
Obtain the title, "Table Tennis God"