After doing around 15-20 quests, a quest will pop up with a requirement stating: WIn a PvP battle. For this achievement you need to START 25 PvP battles. I suggest picking the very easy and easy targets, as a win will be better regarding the rewards. You can also choose to simply attack 25 targets with 1 slinger, and lose. Either way works, though I suggest to go for the win.
You can see your progress if you press Tools-> Achievements.