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This was my second attempt, on the first attempt I was unaware you could target the luopans so was relying on -ra spells to hit them -- which quickly used up all my MP. I had a bunch of Hi-Ethers and Hi-Potions ready to go... but as you can see, I didn't use any.
As Jadey says, just nuke with the opposite element as the Luopan, and when he pops a dark Luopan, nuke with Fire.
Geo-Paralyze was mean to me the first time, so in the 2nd run I made conscience effort to run out of the para bubbles -- locking onto a Luopan (or any target for that matter) and running diagonal backward, or forward will allow you to run, even when your weighed down by gravity if you need to get away from Geo-Gravity.
When the Bygone Geomancer is down to 1 or 2% she will stop casting Geo-Spells so you'll need to pull her into your Geo-bubble and use Concentric Pulse to finish her off.
Also, if you fail, you can just go right back in.