This boss has a fixed battle pattern no matter what mode you're on. Follow that pattern and you’re guaranteed victory.

Doppelganger takes damage only when he’s vulnerable during the time he’s exposed to light. So this is the way to trick him into the light:

There are ‘panels’ (I don’t know what to call them) on the walls around the battlefield. When those ‘panels’ are hit a certain fixed number of times, light will expose. Below lists the number of times to hit them before the light exposes:

Easy: 3
Normal: 5
Hard: 6
Dante Must Die: 7

1. The plan is to hit the ‘panel’ one time less than the number listed above. For example, on Normal mode, hit the light 4 times first and stay there right by it. Shortly, Doppelganger will rush in for an attack..
    
2. Once he gets close enough, hit the panel one last time and the light will expose on him. That is when you attack. Timing is important so try getting used to it to avoid mistakes. Doppelganger doesn’t stay vulnerable for long, so keep repeating it for another 20+ times or so until you finish his life. (Yes I know it's tedious...) And, use Beowulf for an advantage.
    
   

   Note: For Royalguard lovers, you can turn this entire strategy to your full advantage. First, lock on to the panel you are hitting. When Doppelganger dashes at you to attack, be ready to guard it. A perfect guard will stun him, so hit the panel one more time to expose the light, release your lock on the panel, then attack. Do this several times until your rage is full, then release it on him the next time you attack.
    
3. His one other attack is a ground blast. Fortunately, it is rather slow and is easy to avoid; just keep running.
    
4. Cerberus is recommended for this battle. One press of the Triangle button already means 2 hits so hitting the panels will be faster.
    
5. Note: Exposing ALL the panels will turn Doppelganger vulnerable for a longer time, but it is not recommended unless you're playing Easy mode. Doppelganger will forcefully shut the panels down (using a black orb) one by one when he sees that many have been exposed, so your effort will be in vain. However, it is possible for you to deflect the black orb back at him with a melee attack. This will save the panel from being shut and damage him at the same time. In the harder modes, though, Doppelganger learns to deflect it back at you too so you may have to deflect it a few times before it finally hits him.

Hard mode - Video demo with text (2.29 MB)