The thing your doing wrong is not posting a screen shot of the challenge.  

As far as I can see, this is the text of the challenge (simple google investigation)

2.3 Kill an enemy Champion on your first turn and win a battle / 20k Silver 

It means you need to kill an enemy within the first turn...there are other reports that indicate it might be bugged...

Somebody calling himself Trent Larson did report this and was asked to do a request on Technical Support

Well my point is, if you are asking for advice, you shouldn't expect 10 different people to do the same google check to figure out what your issue is so they can respond.

I think "first turn" is literally the first champion going. If you attack an enemy team, High Khatun speed boost --> quest failed.

Mission is not bugged, I completed this last night. I think skadi might be correct but I'm not positive.

Here's an image from an old thread about this:

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This quest is not bugged. Whatever champion goes FIRST is your "first turn", not the entirety of your team.

If you have a High Khatun or Arbiter go first, and they don't get a kill, you don't complete this. Whatever champ goes first must be the one to get a kill.

I can't do this one either, been trying it for the last week. 

I've made sure my champion takes the first turn of all champions in the fight, they kill on the first move and they win the fight, I can't work out what I'm going wrong!

Could you describe the situation more detailed? Wich champions did you use and what moves did you make exactly?

By the challenge i presume you are fairlly new:

here is how to do it:

Build someone with 

All the speed you can get

 The crit rate close to 100

crit damage high as you can.

Go to arena, 

select as oponent the weakest team you can find with only 1 enemy.

You kill them all before they counter attack. 

Done. 

I used if im not mistaken someone like warmaiden and apothecay combined to acchieve this, its pretty easy.

Hi, I've tried so many different heroes and set ups it would be difficult to list all the ones I've already tried

Just now I have used Rhonda, her vs 4 low level champions, I killed all 4 in the first go. None of them took a shot in return. The challenge is still not complete.

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That seems indeed to be abug. I've read about this before somewhere, but I don't find the thread again. I think the mission doesn't complete when you win the whole fight in turn no. 1. So in a fight like the one you showed in your pic, Ronda should kill somebody with her A1 or A2 in the first round and complete the fight afterwards.

Okay, I'll give that a 

Okay, I've tried that, she killed 2 people on the first move of the game and then the others in subsequent shots. Still not completed the challenge

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Tried a different strategy and still can't complete

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I've raised a technical issue but I've not had a response 

So I've just completed the challenge!!

I didn't kill the anyone with my first turn, it was the third turn, does not make sense at all, totally crazy!!

Sorry I didn't get to this until now, been a wild week. I would have loved to see this actually happen. I've heard of folks having issues with it - though very sparingly - but have yet to see a video of it. :(

Glad you finally got past it. :)

I am having this issue... I am attacking first.  Opposing team does not buff. I can attack first and kill enemy in one shot.. and Win the battle but do not get the reward.  The only issue i see is I am fighting a team of 3 not 4 even done it with a team of 2 and 1

This seems to be a problem for me too. I have a warmaiden going first, killing, and it's still not completed. Hopefully we find the real reason or if it's just bugged, cuz I even tried the third turn like what MrsT mentioned above. Yet, not successful.

I have the same problem. I guess it's suposed to do exactly one kill before first enemy turn vs full squad(4vs3 easier than 4vs4)