The Earth Elementum is found at the peak of Mount Gemma. Defeating it completes the feat Heart of Stone and grants you 10 Training Points. The Earth Elementum is more difficult than the Nature Elementum, but nothing that can't be dealt with easily enough with a good strategy.
The strategy is quite similar to the Nature Elementum. You will need at least a couple of decent Miscrits with good defensive debuffs like Sludge. It's best to use three debuffing Miscrits if you have them; weaker Miscrits are okay to use as long as they have good defensive debuffs. Put those Miscrits first in your party. For your last Miscrit, use your most powerful physical attacker.
When the fight starts, just continually debuff the Earth Elementum. You should be able to survive a couple of attacks until it uses Sinkhole. If that attack lands, your Miscrit will die. Just start using the next Miscrit to debuff. The Elementum will occasionally buff his Elemental Defense; this doesn't effect the strategy. You should have no problem removing all or most of its Physical Defense before your last Miscrit comes out to attack. You will (hopefully) kill the Earth Elementum in one hit.
Note: If you are using lower leveled Miscrits, you may need to heal yourself with potions a few times to ensure that you hit the Elementum with enough debuffs. I would suggest removing around 70-80 Physical Defense, but I'm not sure as to the exact number required. It will vary depending on the Miscrit you are attacking with.
Alternative Strategies: I want to briefly mention the other strategies commonly used for people who do not have the Miscrits necessary to utilize my primary strategy. You can debuff the Elementum's accuracy to reduce the likeliness that Sinkhole hits. You can also use Poison attacks to wear away at its Health while you are debuffing it or healing yourself.