Probably super-basic but: take advice the game gives seriously. Galaxy Princess Zorana has no interest in tricking the player, only the characters involved in the story.
Much of this game is about exploring alternative options. Failure is part of the fun. Replaying to find out what changes remains a big part of the fun even after securing one's first win.
However, if Zorana is always failing, consider her studies more carefully. Either she is dividing her efforts up too much, or she is trying to do things that lean on her weaknesses instead of her strengths.
Leave the tutorial guidance on initially, unless familiar with LLTQ or similar games (and consider keeping it on even then).
Concentrating on a few skills is likely to give more insight into the game on early runs than spreading oneself out thinly. Even if those skills are the less useful ones, you won't have to guess whether the skill was simply not high enough.
Time skill learning for when bonuses are available, where possible.
Unless otherwise stated, a tercen is a turn, and most things will only provide one turn's warning. If something is more than one turn away, the turn it happens will be specified. A fivim is a much longer time period.
There are more Electors in some places than others.
Prioritise getting good advisors in knowledge that Zorana isn't going to personally learn (or won't learn much) this run. Consolidate learning Zorana does do in that subject into the fewest possible turns.
Your ship will stay in the same place for the last two turns, which means it can be helpful to stop somewhere that has multiple unclaimed Electors left.
If you have more than 2 options for passing a check, and Zorana fails all of them, make a note of every check. Whether it's a vital test or simply a problem possessing many solutions, you will find you have several interesting avenues to explore on future runs.