The Doppleganger, if no one else knows, cheats. It shouldn't be a secret to you since you have beaten it before (with another character).
Many people like the 1-2 combo Backfire and Empathy. To me it isn't always a good thing. Backfire hurts you if you cast a spell. As a spellcaster, that's what you do. Oh, of course, don't cast backfire while backfire is on you. Guess what, you cast that first, then you probably won't be able to cast empathy without being hurt. Even once the backfire is finished on you, it probably would have been finished on the doppleganger before that time, which it can once again cast on you. Empathy will no doubt be the spell that casts it, but you will still be hurting badly, unless you can evade the attacks.
My suggestion is to use Spirit of Failure, Spirit Shackles, Empathy, Res Signet, Illusionary Weakness, Signet of Capture, Distortion, Physical Resistance. Cast IW before you start touching the stones. Make sure you have full health before touching the last stone.
Start casting Spirits, then Physical Resist, then empathy. Distortion is last.
Once done, just sit back and relax. Spirits, Physical Resist, Distortion and Empathy are totally useless to the doppleganger because you aren't attacking. You will cause the doppleganger to lose energy and give yourself energy. Distortion is an option for you to cast (not necessary). The doppleganger will cast IW and lose life. Since its in battle, no health regen.
Death will occur eventually, and you will be victorious, with lots of life.
I don't know what your 2nd profession is, but whatever you do, don't bring healing skills. IW is the only healing you'll need (if at all). If you have a pet, bring it and only pet skills. Doppleganger has not pets, so you can use your pet to kill it no problem.
Hope this helps.
