This achievement is currently unlocking regardless of if you win the battle.
Enter a versus match with a team full of common pins and watch as this achievement POPs
after the battle.
It goes without saying this may be patched in the future so do it ASAP.
Edit: TheGearGuardian mentions in the comments that you must be at Arena level 2 in order to unlock enough bronze pins to field a team of 8 commons. I did notice it seemed to take a while to get a full team. Thanks for that additional information!