How to open the door in the basement of the academy. Please describe all the steps and tasks step by step. I was able to unlock only the sun and fire. I still couldn't open the dog, cat, moon and ice 

You're supposed to have stars pointing to where you have to go on your minimap/Fae indicating you the right dungeon. If you get lost, the phoenix girl talks to you when you launch the game (and wake up from any sleep? i can't remember that one) for the next step.