The two handed axes are the weapons in the top row of the knight class. To get this achievement you will need to get 75 kills with two handed axes after you have unlocked the second two handed axe, so that is 100 kills total with two handed axes for this achievement.
Free-for-All matches can be good for this as a swing from a two handed axe can kill more than one person with a swing, however these weapons are fairly good in all game modes. I much preferred the second two handed axe while going for this achievement as it has more reach than the first, however you do lose a bit of damage so it is really just personal preference.
Any suggestions for this solution just comment. :D