As a Mo/E I had tremendous trouble beating my doppleganger while he was equipped with any healing skills. Being a computer player he was able to use them very quickly, and matches degenerated into stalemates which lasted ages until his superior weaponry squeezed him into the lead.
I finally countered this by equipping Reversal of fortune and Firestorm only.
reversal of fortune kept me alive when he shot me, and I was easily able to step out of his firestorms. Not being able to move meant that the poor dopple could not dodge my firestorms, while RoF was unable to counter every firebolt that struck him.
Of course, this advice is totally worthless if necromancers have no skills which rapidly deal small increments of damage for a time. Sorry, I don't have much experience with Necros...
Pump up all in divine.
Take DB Use it when you need healing you will get health Because of DF + DB. Doppelganger is a computer. be smarter. Db = Enchantment. Computer will only use it 1 time.
if you are a mo/w
bring flurry, retribution, healing breeze, and bane signet.
cast retribution and healing breeze before you enter. use bane signet refresh healing breeze. do that until he dies. dont use flurry, but the dopple will.