PvP battles are broken into tree types each with different victory conditions. For World Map battles, the Attacker will need to destroy 100% of the Defender's base in order to achieve Victory.
For PvP Quickmatch and Revenge battles, the Attacker only needs to reach 1 Star in order to win the battle. Additionally they do not need any surviving troops in order to achieve Victory. Stars are awarded as follows:
1 Star - 70% Base destroyed
2 Stars - 85% Base destroyed
3 Stars - 100% Base destroyed