The bows are the weapons in the top row of the archer class. To get this achievement you will need to get 75 kills with bows after you have unlocked the second bow, so 100 kills total with bows.
Objective matches can be good for this as opponents will be a bit more focused on the objective instead of rushing in a attacking you. You might as well use the shortbow (second bow) due to the achievement of firing 10,000 shortbow arrows.
Any suggestions for this solution just comment. :D