Here is the full list of all 13 Hikikomori No Chuunibyou achievements.
Finish the tutorial (without dying).
Complete the first level.
Complete the first level without dying.
Complete the second level.
Complete the second level without dying.
Complete the third level.
Complete the third level without dying.
Complete the fourth level.
Complete the fourth level without dying.
Complete the fifth level.
Complete the fifth level without dying.
Distribute a flyer while running an errand for the pharmacist.
Finish the tutorial after dying at least once.