Nobody responded to my previous post so I'm going to try again.

I've been stuck on Minerva's research lab for forever. how do I clear it?

I don't believe there is any "easy" way to get past her lab. What I can say is that you should go through the classes in the academy again and pay attention to what's said, and then save right before her fight. In order to get past her trials, you end up needing to remember the lessons you attended during the day, such as the multiple choice questions asked in the life magic class, as well as puzzles from previous portions of the game. Nothing changes from attempt to attempt, so you can see what works, take notes, and try again without the frustration of having to figure it all out over and over each time you repeat. Unfortunately, the whole process is timed, so you'll eventually have to do it all fairly quickly.