The second option is correct. Here's the breakdown.
First, you hit with a power attack. This triggers Cornugon Smash.
Second, you make an Intimidate check. Since this check explicitly happens after your first attack is finished, Shatter Defenses cannot come into play. In order for Shatter Defenses to work, you need to hit an opponent who is shaken, and the opponent is not shaken here until after the hit has gone though.
Third, you make another attack. This attack will activate Shatter Defenses. However, this attack is made against your opponent's non-flat-footed AC. Since you need to make your second attack roll before the attack hits, and the first attack cannot have activated Shatter Defenses, this attack has to be made against the enemy's normal AC.
The reason that the second attack is against normal AC and not flat-footed AC is that Shatter Defenses doesn't take effect until you have actually hit your enemy. You make your second attack roll before you hit with your second attack. Since Shatter Defenses requires you to hit before it works, the attack roll for the second attack is made against normal AC, not flat-footed AC.
The third and later attacks are against flat-footed AC.
I understand your confusion, but the real answer, like in many cases, is "whoever wrote/edited this feat did so poorly". The interpretation favoured by all of the answers here is assuming that the feat is written poorly, but that it works like every other feat in the book. Namely, that it provides an effect after a hit, rather than passively providing a benefit that triggers under a particular circumstance. If you, as a GM, want to read it differently, no one is stopping you. If you want to do this as a player, make sure to ask your GM in either case, since this involves a poorly worded feat.
The core reason that the second interpretation is more likely to be correct than the first is that there are few to no feats that work like the first interpretation implies. Feats like this are almost always active, and require an action on the part of the player to activate, rather than working passively.
To give an example: Suppose you had Shatter Defenses, but didn't have Cornugon Smash. On your turn, you full attack an enemy. On your Wizard friend's turn, he casts fear. On your enemy's turn, he runs away, providing an attack of opportunity. With interpretation 1, you would attack his flat-footed AC, since he is currently panicked and has been hit by you this round. This doesn't work with the way feats typically work, and it doesn't work with the fluff description of of the feat, which says that it
leaves opponents unable to defend themselves if you strike them when their defenses are already compromised.
With interpretation 1, you aren't striking a foe whose defenses are already compromised. You are striking a foe, and then his defenses are becoming compromised. While the wording of the feat may be unclear, it makes a lot more sense that it requires you to hit a foe that is already shaken than otherwise.
Looking deep into the spell
The spell states that it is an illusion (figment) [fear, shadow] spell, meaning that it has two parts the [fear] and the [shadow]. The spell goes on to describe that the shadow part has a quality that obscures vision and provides concealment, that much is understood. The fear portion of the spell is the "Illusion of misty vapor inhabited by shadowy shapes that arises around you". The (figment) tells us this "A figment spell creates a false sensation. Those who perceive the figment perceive the same thing, not their own slightly different versions of the figment. It is not a personalized mental impression." This tells us that the spell does not change, and that the shadowy images and shapes that dwell within the mist do not change or get worse, they are the same for everyone.
This means that the spell is not doing physical harm to your body, but instead the images are scaring you mentally (The wisdom damage). It is not a gaseous vapor that you are inhaling every 6 seconds, it is a shadowy illusion spell that has a specific impression meant to mentally scar you. You are either fooled by it or you are not. You don't simply believe that the shadowy shapes and misty vapor is indeed a spell fooling you one second, and six seconds later completely believe they are real. Cloudkill requires a save every round because you are still subjecting your body to the poisons, the illusions on the other hand are figments, they do not physically harm your body.
Fear effects are compounding.
The bottom of the spell description states that "All creatures within the mist must save or take 1d2 points of Wisdom damage and gain the shaken condition." Under the fear description (page 563 cr) it states "In most cases, the character makes a Will saving throw to resist this effect, and a failed roll means that the character is shaken, frightened, or panicked.", it goes on to say that "Fear effects are cumulative, a shaken character who is made shaken again becomes more frightened, and a shaken character who is made frightened becomes panicked." This addresses the "shaken" part of the fear spell.
Final Conclusion
A creature would only make a save. If they fail their save, they are mentally scared and take 1-2 points of wisdom damage on top of being shaken for as long as they remain in the mist. Leaving the mist after failing a save would mean that the character still keeps the wisdom damage, but loses the shaken effect. Should they re-enter it, they would inherit their last fear effect (Shaken, Frightened, Panicked). Fear effects are disbelief based, which means that the second a character makes a successful Will save, they no longer have to make another save, they already know that the spell is just an illusion.
However
It does state that fear spell are compounding, and fear effects go from Shaken to Frightened, Frightened to Panicked. As a DM you could have players make multiple saves should they fail their first one to determine if the level of fear increases, but that is part of the spell is only in place should they already have the shaken condition. The Figment part of the spell suggests that because the spell does not change, the player would not take consecutive wisdom damage, the damage is already dealt upon seeing the shadowy shapes. It is up to you as a DM to decide the final ruling.
Best Answer
The description of mithralmist shirt is somewhat vague. It not necessarily creates a fog similar to that of Obscuring Mist spell (item's prerequisite to be created), but 'billowing silver mist' it creates still lacks some info to be clear enough as a separate standalone effect.
As written it neither doesn't interfere with your attacks when you shoot from the space filled with it, nor doesn't interfere with your attacks when you leave that space. Also, as written, it grants concealment only to you (sireously, that may be the reason why it doesn't interfere with your vision with no caveats). Those assumptions are questionable while possible. In this case your rogue may shoot freely. But what happens to ranged attacks of those entering his bank of mist is mostly left on DM's mercy.
Another way to interpreate given item is to assume it creates a bank of fog similar to that of it's prerequisite spell. That bank just happens to be only as large as your space is and is in that space when you activate the shirt. That way whole discriptive text stays largely true, but we know what to do with cases not touched by it.
If we go this way, either rogue or anyone entering the fog may fire their bows with no hindrances. Obscuring Mist confers concealment depending on the distance between1 creatures in squares containing the fog. You may treat that as if armor owner was standing on the border of regular Obscuring Mist's effect. As your rogue (or any creature for that matter) stands right next to the border2 of a clouded area there actually are no squares of fog between her and her target. So her target gains no concealment.
For a creature to see into a square that creature's line of sight must be traced into that squere. So a target's squere also counts as part of a distance.
If your rogue is larger than medium, things may got more complicated. As there will be more than one square to enter, entering creature may position itself in a way it isn't adjacent to the border with respect to it's target. Not to mention, if armor owner himself moves, he may do the same.