From a conceptual level I'd probably want to print out the sequence of actions/skills the player used in each battle to a database or a spreadsheet, along with data about the "result" of the battle (such as victory/defeat, how many turns it took, and total damage/healing dealt to characters). You could then run queries on some of the best and worst results to see if there was a pattern in which actions the player was chosen - for example, if there's a broken strategy that involves stun-locking enemies, you'll see the skills involved over-represented in a search for Very Low Damage to Characters.
Ultimately, though, unless you're designing a
competitive game where every option needs to be almost perfectly balanced against most other options for highly skilled players, all of this is grossly unnecessary. For the balance of a standard RPG, all you really need is general feedback from 20 or so playtesters. They'll let you know if they find techniques that make the game too easy, or a difficulty spike in the power of monsters from one dungeon to the next frustrates them. What's even better is if you can watch a few of them play through, either in person or by having them record their play experience. Talk to them as little as possible as they play through - let them (try to) figure out everything on their own.
From there, you'll know what's wrong in your balance, and you'll probably have a good idea of
why it's imbalanced as well. So you just need to make a change to address that issue. For example, in
timeblazer, I noticed that while my mage's Heal skill felt useful, its high MP cost (designed to prevent spamming) was also making it hard for her to use her more fun Damage spells. So I reduced its MP cost, and created a "charges" system (she can only use the Heal 3x per battle) to address the spamming issue instead. Someone let me know that the large number of unique mechanics in a certain boss fight felt intimidating, and several testers let me know that same battle was too difficult, so I changed up the battle to introduce the mechanics one at a time throughout the battle, instead, with the first few turns being basic and giving the player time to get some buffs up before the boss brings out the big guns.
As a bit of extra advice,
this post addresses some design tools you can use to give yourself a wider "balance target", so that the gameplay is richly satisfying even if your balancing isn't exact.