The Earth Elemental appears as the final challenge in the Mines area (the first set of levels you have access to).
As soon as you start the boss level, run towards him and hold your attack button as he hurls rocks. As the rocks fall, run left to the wall then back again to avoid them.
Now he'll start wandering left to right across the screen. Attack him as he's going away from you, jumping over him as he comes back towards you.
When he stands still, he'll start his third phase: Causing stalagmites to rise from the ground where you're stood. I recommend holding down the attack button and jumping in time to avoid them.
You should easily put him down during this phase.
For the record, I was playing the Rogue, pumping points into Critical, with the Ice Sword and the third suit of armour.