I bought my first weapon for my pet and I moved it to the Armory, but I don't know how to access it. ;-;

http://subeta.net/games/battle/index.php

Or you can go to games and scroll down to Battle Coliseum and access your armory from there.

Or

Click Explore, head to Sacred Lands, Click on the large circular building and there's the Coliseum as well.

Or if you have the battle pet widget, clicking on the blaster takes you to the armory