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