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I'm not sure how much of this is common knowledge by this point but now that this video has finally been encoded (took it long enough) we can share the method The Last of Us LS on Asura used and still use to pop both Perfidien and Plouton in the same Vagary run. The run itself, in the Duskbrood Gate, begins at 5:00, feel free to skip to this part. Audio has been removed but doubt you would have needed it anyway.
Here is a video recording of a run we did last night where we cleared both Perfidien and Plouton in the same run. Here we detail our method of popping both NM in the same run. The first two stages are the same for both NMs but the third stages are slightly different. We upgrade both KI at the same rate as we go, meaning that we do not rush all the way to Perfidien then restart for Plouton as it is much easier
Stage One: Elemental magic kills of the opposing element to which we are fighting while taking care TO NOT ONE SHOT. Doing this with the correct element (water on fire elementals, fire on ice elementals etc) enough times will upgrade both KIs. Either doing the wrong element (as I think we do at one stage in the video) or having a death will severely disrupt this part of the process.
Stage Two: We then do various skillchains between our two BLU and MB the proper elements off said skillchains to achieve the second upgrade for both KIs. You notice in the video that when we fight the Ice Elementals we have our two BLU perform Liquefaction and have our mages MB with LOW TIER fire spells to increase the number of MB's per skillchain. We're pretty certain that it is the NUMBER of MBs and not the DAMAGE they do that causes this upgrade for both KIs. As you can see in the video we run out of Ice Elementals so we move to the Earth Elementals and adjust the skillchain to Light and MB wind damage (see the pattern here?). We normally pop both NM before we have to go to the Wind Elementals but as I said earlier, we made a mistake earlier in the run but still pulled it off.
Important: At this stage we had our two BLU take their 119 swords off and use low level weapons to ensure that the Elementals we were fighting did not die before the skillchains went off. I, the GEO with the two BLU, went with them and put Indi-Precision and Geo-Torpor down so they could hit their targets reliably and to Dispel the Ice Spikes and Stoneskin off the Elementals.
Stage Three: At this stage the BLM do absolutely nothing. This stage involves multiple consecutive skillchains on a single elemental, the type and element of the SC doesn't matter. Three skillchains involving four weapon skills pops Perfidien and four skillchains involving five weapon skills pops Plouton. No particular job is needed, just two or more melee's that know how to link various WS's. As you can see from the video we did Red Lotus Blade -> Seraph Blade -> Red Lotus Blade -> Flat Blade to pop Perfidien and just added a Savage Blade at the end to pop Plouton immediately afterward.
Timestamps
5:00 = Run Begins
6:10 = Blue Mages equip low level swords
9:10 = Ashen Wings upgrades to Lv1
16:00 = False King upgrades to Lv1
16:50 = Stage two of Ashen Wings begins
21:10 = Ashen Wings upgrades to Lv2
21:40 = Stage two of False King begins
28:20 = False King upgrades to Lv2
Upgrade process for both KI is now completed.
31:00 = Skillchain begins to pop Perfidien.
31:20 = Perfidien pops.
38:00 = Perfidien defeated. No 1-hour abilities used. 15 minute time extension.
40:27 = Skillchain begins to pop Plouton. First skillchain fails due to uncapped Haste on the BLU.
40:50 = Plouton pops.
54:30 = Plouton defeated.
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I understand that there may well be other methods for popping both of these NMs but in our experience this is the easiest method out there. Glad to share it with you all.