I have the exact same issue. It is only Aion's version of Gameguard that causes problems. The issue exists in both the NA Beta version as well as the Aion-C (China) version. The only way to play without having BSODs, Gameguard Error 114's and complete system instability is to disable the "Self Defense" feature in Avast, which can be found in "Program Settings", "Troubleshooting", and then check the box titled "Disable avast! self-defense module", and then click OK. It will ask you if you're sure. Say yes.
While I HATE having to cripple my AV just to run a game, it is the only way to actually be able to play it.
Would be very nice if Avast can work with Gameguard and/or NCSoft to figure out a true fix that doesn't leave their customers vulnerable.