I lost to the lvl 20 avatars 3 times before I beat the crap out each of em.
What I did:
-Capped summoning skill. -Sub lvl 10 WHM. -Bring Yagaudo Drings (4-5). -Hi Ether (2-3). -Hi-Potions (5-6 when I started 2-3 once I knew how to kill em).
-Elemental buff before fight and shell + protect. - Eat Food, depends on race, for Taru fish kababos or boiled crab.
Enter the crystal, buff up, eat food. Don't use ether at this point. Go half-way up the ramp and drink one of your Yags, then summon Carby. Walk within casting range the avatar, now this is risky so you don't have to do it, but this is what I did. Cast Dia on the prime, sic carby one it, and run back down to the start crystal. Carby should grab hate in this time. Run away, even if you can't see him, and watch his life bar, when it goes away, recast he'll auto attack the prime. I had carby use poison nails, that seemed to help a little. Once the Prime is down to 50% HP hit your first Searing Light. Make sure that you have refresh active. Carby will not dissapear completely you'll have about 2-5 mp left, use an ether and keep running and summoning. When Searing light is ready again use it. The prime should go down by then.
Side note: The greatest one of these was Ifrit. I had used SL X2 and carby was gone and the avatar was punching me so i couldn't re-cast. I had 15mp left. Enough for another try at carby, or for banish, so i banish him and pull out my stick and start beating on ifrit. and I won. =P