I'm a R/Mo and I struggled to beat the doppelganger with a number of different skill combinations.
I tried doing it with my attributes split evenly between marksmanship and healing prayers, and removed all skills except healing breeze, and did it with about 90% health left. My doppelganger didnt use it once, and just kept attacking me.
Not sure if it works for everyone, but it did for me.
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