Here is the full list of all 14 魔塔少女/Magic Tower & Maidens achievements.
Enter the desert for the first time.
Enter the jungle for the first time.
Enter the suburb for the first time.
Enter the hell for the first time.
Reach level 30.
Reach level 40.
Reach level 50.
Reach level 60.
Reach level 70.
Meet Sheesa for the first time.
Meet Livviel for the first time.
Meet Meeley for the first time.
Meet Vivian for the first time.
Meet Ive for the first time.