PVP (player vs player) battle area can be accessed via the blue Battle [戦闘] icon.
Select the green icon [手合いバトル] to enter PVP.
In the PVP window, your opponents are listed on the right. Select an opponent and enter the battle.
The battling process is similar to the Main Battle sequence.
PVP is a quick way to level up your unit members. It does not level up the players' ranks.
You can PVP twice a day.