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