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