Unfortunately, this isn't a bug and is working as intended. You are still effectively having one dungeon run, but with double the energy spent and double the rewards. 

I understand that you are doing 1 run and using double energy and getting double rewards, However you are still effectivly doing 2 battles.

You get a reward for killing the boss, you get 2 rewards on super raids, therefore you killed the boss twice.

If that's not how it works can you explain why the quest for faction wars works correctly (see images below)

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If it counts the faction war battles as two seperate battles, using double the amount of keys and getting double the rewards and not counting it as 1 run, then why doesn't it do the same with Dragon's lair and the boss quest?

It should use the same principles in both locations for both quests.

It should either count the battles for the beat the boss quest and the faction wars quest as 2 battles or it should count both of them as 1 run and not have different results when using super raids.

Therefore my previous arguement still stands, If you run a dungeon on super raids and it counts as 2 battles it should advance the beat a boss quest by 2 and not 1.

So either the beat a boss quest is bugged or the faction war quest is bugged they can't both be working correctly, and I for one am saying that it is the beat a boss quest that's bugged.

Faction Wars and content that requires energy are treated differently - as they arguably should be - due to Faction Wars using a finite resource, while energy is potentially endless. That detail is important, especially in CvC. 

It also does seem a bit trivial, in needing to do a few extra dungeon runs to finish off that quest.

But again, not a bug.