I can tell you what you need to do in each stage. I played this fairly recently so I remember most if not all of the tricks. But much of the fun of the game is figuring it out yourself. I didn't figure out how to beat the first round until my second playthrough, when the pattern finally became clear to me.
The tutorial explains that you need BOTH sufficient team power and the correct ruleset. You also need the right team members. Fail any check and you lose. To win, you have to talk to EVERYONE, puzzle out their hints, and maximize your team power (again, through talking to everyone, often multiple times). The defeat scene usually gives a strong hint as to what went wrong, and what you could have done differently to win. It is possible to witness the star events in the wrong order and lock yourself out of a victory; it's a sort of dice roll to further stack the odds against you.