Here is the full list of all 18 Table Tennis Toon! achievements.
Beat Amy in Story Mode for the first time and unlock her story
Beat Jackie in Story Mode for the first time and unlock her story
Beat Jolleen in Story Mode for the first time and unlock her story
Beat Michelle in Story Mode for the first time and unlock her story
Beat Ninja in Story Mode for the first time and unlock his story
Beat Ortiz in Story Mode for the first time and unlock his story
Beat Pelegrini in Story Mode for the first time and unlock his story
Beat Rosales in Story Mode for the first time and unlock her story