So first of all you need this map.
Setting up an alliance is not easy, I was building for my LS first run for over a week. I ended up with this alliance for the 2nd run after I used /yell to fill in the blanks.
Tank Pt - (Burtgang) PLDx2, WHM, BRD, GEO, BLU (switched BLU from mage pt to tank pt after first run for Indi-Focus on BLM)
Mage Pt - BLMx3 COR SMN GEO (focus on MAB and MACC. SMN buffs/heals BLM, can be substituted for a SCH though)
DD Pt - SAM RNGx2 BRD COR WHM (originally had RDM instead of WHM for flurry II, haste II (etc.) but the SAM kept dieing due to lack of cures. SAM should be using the appropriate skillchains when possible)
No buffs on entry, just run to the first camp (I-6 corridor) and don't cast anything on the way (eles are magic aggro). When everyone gathers, buff ASAP, and have PLDs voke Ice Elementals to the group. Kill slow to begin with, then have PLDs magic pull eles to gather more after the alliance has got into the flow. (Don't overwhelm the alliance right from the start, that's not cool.)
On our first run, we killed the earth elementals as well, but it turned out to be a waste of time. So just ignore and run to the next camp at I-7. Best to keep the mages in the corridor so they don't magic aggro. So the first NM is an Umbril, and the elementals surrounding it appear to aggro by sound (just a guess, they have long range also), so we decided to give our main PLD Mazurka (movement speed), and Sneak/Inviz. He would aggro pull the Umbril and run out of range before the umbril hits him so the elementals don't aggro. It can be tough to pull without aggro, so be prepared for the worst.
If the elementals aggro, then let the PLD run the Umbril past the alliance and let him tank it down the corridor (and down the slope), while the rest of the alliance SLEEPS (no one was doing sleeps on our first run, which was dangerous) and nuke the elementals down. Repeating sleepga and lullaby is a must, as well as keeping stoneskin and other buffs up. Once the elementals are dead, everyone focuses on the Umbril. If the Elementals did not aggro, then great! You can kill those later after the umbril.
The umbril is quite easy. It can Doom the PLDs so their WHM should be ready for that. I suggested Light Skillchains with Fire, but I didn't check to see what the alliance ended up using. The SAM should back off if they are taking too much of a pounding.
After Umbril/Elementals, the door should open to the south. Next camp is the room in L-10. Have the PLD hunt down all the Water Eles in the area. Once they are all dead, the alliance can set up camp in the K-10 corridor. Similar thing to the Umbril, Mazurka/Snk/Inviz the PLD, hope the PLD pulls Insidivo without aggro. On our run, we had the elementals aggro with the NM, so the PLD kept the NM close to the room, while we slept/killed the elementals quickly.
The Pixie NM is quite powerful. We focused more on Darkness Skillchains and Ice. At some point, Insidivo will do a crippling AOE attack with a LONG range. Even if you are stood as far back as possible to nuke/fire, you will still get hit (probably). Healers should be prepared to cure everyone at that moment. Minimize deaths as much as possible.
Once the NM and eles are dead, the door will open in the room. Kill the dark elementals (watch out for Sleepga!) and then you are ready for Putraxia. Camp in the Dark Ele room. Give PLD mazurka and they can pull the boss to the room. Putraxia isn't too difficult, we used Darkness skillchains and Ice. Told one of our GEO to Bolster at 75% (ish), and the other one at 35% (ish). Died rather easily. Shouldn't pull this if you have five minutes or less on the clock after the Dark Eles.
Not the greatest guide ever. Just kinda threw it out there. Now I need to set up my Vagary run for tomorrow :)