It's time to Break some bosses.
Each of the normal bosses in the game is subject to a mechanic called Breaking. This is a simple but useful way for you to lower the power of a boss - as long as you don't get fed up by its Barrier.
When a boss fight starts, any boss-type enemies are surrounded by a Barrier (minions are unaffected). This Barrier lowers damage taken by 90%; you can't really do much of anything until that Barrier gets shut down. Thankfully, this is easily achieved with a few turns of normal attacks. Ten normal attacks, to be precise, will lower all Barriers in a battle and allow you to pummel any bosses into oblivion.
But let's say you have a Rotting Lunch kicking around, or you think an boss is weak to Fire, or you've been itching to Charm an enemy with your Chaos mage's cooled-down Seduction spell. That's where Breaking comes in.
Each boss has one specific action or cluster of actions that will Break its Barrier, shocking it into a weaker state. The boss will then have lowered stats, making it only a nasty threat instead of a terrible one. These actions can only be performed while the Barrier is up, so you'll need to balance your just-in-case normal attacks with experimentation. A boss's weakness might be a certain status ailment, or being struck with a critical hit, or having a character turn into a vampire... anything goes.
Sound completely arcane? Don't worry - it's an easy flow to get used to. Bosses don't start utilizing their super-strategies until their Barrier is down, so while they're still hurting you, you can focus on discerning an enemy's fault line without worrying too much. On top of that, bosses will drop hints as to what you need to do (even if you have to keep it in the back of your mind for your next encounter!), party members will throw in suggestions, and if you influence certain denizens of the Edifice, they'll help you conquer the Barriers.
Have fun figuring out every boss's Breaking point! There's over thirty unique boss encounters to analyze, so you should probably get started.