From the web home page, click the [Explore] button. Then click the [Trading Battle] button, which will take you to the Battle list in the Battle Trading menu.
From here, you can check [Battle list], [Official recommendation], [My battle], [History of participations], and [History of creations].
[My battles] contains the history of both the battles you participated in and ones you created, as well as upcoming battles and ongoing ones.
Please be aware that only Trading Battles that ended already are displayed in [History of participations] and [History of creations].
