Tactical Challenge
Arena is the Player versus Player mode of Blue Archive. The arena mode is unlocked once you clear world 6-1 on the main story maps and it puts your team versus the enemy team. It is often reccomended to unlock this mode as soon as you can and attempt to climb using refreshes as far as you can until you can't climb anymore.
The blue button to the left allows you to see your battle history of who you attacked and who attacked you while the blue button to the right allows you to set up a defense team. This is really important so make sure to constantly update your defense team if you level your units and their skills because players in this mode will be fighting whatever team you set up here.
You will also see two yellow buttons here with the top one being to collect credits. You can see how many credits you are generating per minute and how many credits you have stored up. If you press the button then you will collect all stored credits and add them to your total, remember to do this every day. The yellow button below it is to collect PVP rewards for the day and this button will only light up once a day at 14:00 JST. The rewards that you can collect by clicking this button depend on your current rank so it is reccomended to do all your PVP battles then press it to collect rewards based on your current rank.
To the right, you will see three players at random from the people you can attack. You can only see their team leader and supports, the rest is only visible after you attack them from your battle history menu. Clicking on the top right button will refresh this list and clicking on a player will take you to the preparations screen where you can set up your team that will attack the player. This team is different from your story teams and defense teams so pick what units you want to use to attack and then attack. The battle will be an AI vs AI fight with zero player input or control with the result being determined the moment you pressed attack. If you lose connection or quit before the match is over then you will be awarded a win or defeat based on the calculated result of the match without it affecting the outcome.