
Seems |

Cornugon Smash reads, "When you damage an opponent with a Power Attack, you may make an immediate Intimidate check as a free action to attempt to demoralize your opponent."
So, if I hit an opponent multiple times with full-attack, does Cornugon Smash activate on each hit and I get an immediate Intimidate checks after each hit, or is it only once per round?
Shatter Defenses seems to imply the latter, as it reads, "Any shaken, frightened, or panicked opponent hit by you this round is flat-footed to your attacks until the end of your next turn. This includes any additional attacks you make this round."
You can't use Shatter Defenses on "any additional attacks you make this round" if you're not making an Intimidate check on each hit. This seems like an incredible drag on combat, unless you just starting rolling an extra d20 with each attack in case it's a successful hit.

Ryze Kuja |

Every time you cause damage with an attack you're using Power Attack with, you can attempt an Intimidate check; so if you do a full-attack action that gives you 4 attacks in a round and you successfully hit with 3 of them, you would make 3 Intimidate checks during that round.
If you've successfully Intimidated your opponent via one of these Power Attack/Cornugon Smash attacks, and they're shaken because of it, each successful hit would cause Shatter Defenses to apply, and the target will remain Flat-footed to your attacks until the end of your following round's actions.
So, in theory, as long as you keep landing Power Attack/Intimidates and successfully hitting your shakened target, they will remain Flat-footed, at least until you miss with all your attacks for two straight rounds.

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Intimidation focused characters can turn insanely powerful if you stack all the right things, like Shatter Defenses, the Cruel weapon enchantment, maybe 5 levels of Unchained Rogue to get the skill unlock for Intimidate, etc.
Of course anything mindless, or immune to fear will just laugh at you...but the majority of things are not immune.