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