Here is the full list of all 42 Cute Puzzle SP (Naked Story Ver) achievements.
EasyMode LV01 Achievement
EasyMode LV02 Achievement
EasyMode LV03 Achievement
EasyMode LV04 Achievement
EasyMode LV05 Achievement
EasyMode LV06 Achievement
EasyMode LV07 Achievement
EasyMode LV08 Achievement
EasyMode LV09 Achievement
EasyMode LV10 Achievement
EasyMode LV11 Achievement
EasyMode LV12 Achievement
EasyMode LV13 Achievement
EasyMode LV14 Achievement
NormalMode LV01 Achievement
NormalMode LV02 Achievement
NormalMode LV03 Achievement
NormalMode LV04 Achievement
NormalMode LV05 Achievement
NormalMode LV06 Achievement
NormalMode LV07 Achievement
NormalMode LV08 Achievement
NormalMode LV09 Achievement
NormalMode LV10 Achievement
NormalMode LV11 Achievement
NormalMode LV12 Achievement
NormalMode LV13 Achievement
NormalMode LV14 Achievement
HardMode LV01 Achievement
HardMode LV02 Achievement
HardMode LV03 Achievement
HardMode LV04 Achievement
HardMode LV05 Achievement
HardMode LV06 Achievement
HardMode LV07 Achievement
HardMode LV08 Achievement
HardMode LV09 Achievement
HardMode LV10 Achievement
HardMode LV11 Achievement
HardMode LV12 Achievement
HardMode LV13 Achievement
HardMode LV14 Achievement