First of all, I'll copy/paste MY guide to defeating it as a ranger (primary OR 2ndary class)
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Tired of losing to doppleganger? Need that bonus from ascension? Here's my answer to all your troubles. Load up on preparations. Yes, that's right, just get around 5 preparations. Then get 3 attack skills. As soon as it starts just use your attack skills on him while he uses EACH AND EVERY PREPARATION you equip. That's right, now you get around 15 sec of free attacking. I killed him in 8 sec on my first try (Of using this strateagy). Enjoy that 50,000 xp AND the bonus xp from killing him in under 50 sec!
Mesmer: The by far easiest way to defeat doppleganger as a mesmer is called pacifism. Picked this one up as a guild member was helping out another... He said it worked great, but I'll let you be the judge of that! So basically, keep using Spirit of failure and empathy so they take dmg after evry attack and give you energy when they miss. Equip a healing spell as well. You dont really even have to attack. Just sit there and let him kill himself (and hurt you) as you cast the 2 skills and heal yourself. Having a higher ammt of Domination magic will make this go by quicker (Helps for the 50sec bonus).
Elementalist: This is pretty simple... Don't bring any healing spells as this will make it quite difficult. Use Fire Attunement at teh beginning. Use meteor shower and fire storm to bring him down a lot. Use your base attack and wait for em to use firestorm. then, MOVE out of the way. Then finish up with flare, your base attack, or anything else you happen to be carrying and you've got him beat! That wasnt so tough eh? This is by far the most obvious way to beat your doppleganger out of all of the classes.
Warrior: One of the EASIEST ones in my opinion. My friend reccomended this method to me (My 2nd character was a warrior) All you need to bring is Frenzy. Let the doppleganger use it on himself and just kill him with your standard attack. (He will swing 25% faster but will take double dmg, so you'll have half of your health left at the end (Give or take))
Necromancer (Works well if necro is your 2ndary as well): Equip all heath sacraficing skills. Use ones like awaken the blood, dark fury, malaise, signet of agony, and defile flesh. Dont use these, let doppleganger use em. Another method to make him kill himself! I tried this out on my R/N and it was another extremely easy victory!
Monk: Aaah, monk. The one we all fear! How do you kill someone that does no dmg? heh. Here's how I did it (My 3rd character) Equip vital blessing,banish, bane signet, and symbol of wrath. Right before the cutscene, use vital blessing (Still in effect after the cutscene). When he tries to use vital blessing, use the bane signet, then use banish and symbol of wrath on him. He'll die in no time! One of the trickier ones, but this should do the trick. Did for me and a friend of mine!
In case you were wondering about my 4th class (Not mentioned), which you most likely aren't, hes an R/E PvP character, so I never had to face doppleganger as him, but I dont think I'd have a problem. heh.
*edit 3 of these are from friends (ele, warrior and necro) I found out the monk one and the ranger one, and I overheard a guild member explaining the mesmer one.
*edit number 2... If your monk was lev 13, you most likely wouldnt be at augury yet. If you were, you would have to use a strategy for your 2NDayr class. It would be EXTREMELY hard to beat doppleganger as a level 13 monk unless you used your 2ndary class.