Each Henchman Moogle absorbs damage from one element. The element each absorbs is random.
It appears that Henchmen Moogles that spawn absorbing Thunder-element will be resistant, if not immune, to Stun from all sources. The same may apply for enfeebling magic of other elements against Henchmen Moogles of the same element.
The Henchmen Moogles that spawn absorbing a particular element may also possess a potent Magic Defense Bonus against the element they're strong against. For instance, a Fire-typed Henchman will take significantly less damage from an Ice spell than normal.
Riko Kupenreich will repeat the above behavior two times before he enters his final phase, at which point he may be defeated.
Riko Kupenreich appears to be especially weak to skillchain damage, taking 1.5-2 times regular skillchain damage for two-part skillchains, and more for multi-part skillchains. (See the Talk Page for details.)
Shadow Images will provide minimal protection during this fight. /NIN is not recommended for virtually any job.
It is possible to wipe and Reraise during this fight, as long as party members are outside Riko Kupenreich and his Henchman Moogles' agro radius (by the entrance). Wiping multiple times is not feasible given the time constraint.
It is also possible to rest while Riko Kupenreich is healing himself. If the Henchman Moogles have been defeated before he rejoins the fight, he will not aggro if the party is resting by the door.
It is possible to prevent Riko Kupenreich from being Cured to 100% during each phase, though it is unconfirmed what triggers this. It appears that placing enough Damage Over Time effects on Riko before he retreats may halt his Curing. Players also speculate that the faster the Henchmen Moogles are defeated, the less HP he will recover.
Note that if Riko rejoins the fight with less than 100% HP, he will follow all of the above behavior at the new %HP intervals (e.g. if he starts with 75%, he will use Draw In/Crystalline Flare at 50% and retreat at 25%).
It is possible to protect members from Crystalline Flare by generating no enmity (and thus not triggering Draw In). Additionally, in the final phase, it is possible to move all but one party member out of range of Crystalline Flare.
Riko Kupenreich: Oh, and don't worry. That loan contract I wrote up for you was just random scribbles on a scrap of parchment.
Riko Kupenreich: I would suggest that you stay out of debt in the future, kupo. Live within your means and all. As the old proverb goes, a frugal moogle is a happy moogle!
Riko Kupenreich: Allow me, though, to present you with one last luxury...the Crystal Prize in our regrettably cancelled Mega Mog Bonanza-Rama-Palooza, kupo!
Riko Kupenreich: Consider it an apology for this whole hullabloo, and a token of enduring goodwill between adventurers and mooglekind, kupo!
Riko Kupenreich: To tell you the truth, Uncle Riko's been doing a lot of thinking these past few minutes. Why, I believe I'll give up my moneylending operation and devote the rest of my life to charity. Rent-free shelters for orphans! Food kitchens serving piping hot turtle soup to the poor!
Riko Kupenreich: After all, what are material possessions worth, when weighed against the bond of true-blue loyalty and friendship shared by moogle and master? A lesson I've finally learned...thanks to you, kupo.
Toto Kupeliaure: Oh, h-h-hullo there. Well, it seems this whole per-dicament has been un-complificated. U-u-um... Dad should be b-b-back from vacation soon, and I'll t-tell him you've been model tenets in his obsolescence.
Moogle: Phew, kupo. This time we've really resolved things once and for all!
Moogle: It wasn't easy, but you know what they say. "That which doesn't send your Mog House crashing down into a heap only makes its foundation stronger, kupo!"
Moogle: Thanks to Riko and Toto's hijinks, I've come to realize more than ever just how fortunate I am to have a master like you! Promise me that we'll remain the most faithful of friends forever, kupo!