Regular enemies: burn your specials, they melt, do coup de grace as necessary. You win.
Bosses: cycle through specials to perform max stagger damage and r1 any major attacks. When staggered, limit break to increase basic attack dps and heal, spam square while your specials refresh. When stagger finishes, cycle through specials again to re-stagger. You'll typically have full limit meter again by the next stagger.
That's about it. There's not much asked of you in terms of timing, reactions, learning patterns, or execution. It can be handy to do the wind counter or heatwave projectile counter at times but you can easily ignore that and burn all your specials whenever they're off cooldown to get the same result.
It's mechanically too simple. The bombastic major boss battles are cool because of how cinematic and dynamic they are, which elevates them. But the systems are not nearly as good as they need to be for a character action game, and the RPG systems are too stripped down to make up for it.