The Mount Shop in Wartune is a place that allows you to purchase mounts with Beast Souls. It seems like there are not many way to get beast souls for free, but there are several ways to get them without purchasing anything!
Getting Beast Souls from Mini Games:
Every day in the Gamebox there is a new game to play. Playing games gives you a chance to get Nickles. Every day what you can exchange nickles for different items. Most days beast souls can be found in this exchange. 10 beast souls for 100 nickles.
Getting Beast Souls from League Insignia:
Make sure to do Team Arena daily. Win or lose, you will get League Insignia. For every 3k league insignia, you can exchange for the Venomous Leopard card. If you have already activated this mount card, you may recycle it to receive 120 beast souls. Arena rewards come out every week. You will get extra league insignia when these rewards come out. However, league insignias expire the last day of the month so make sure you use them.
To activate a mount card, double-click on it. If you have already activated it, a window will pop up prompting you to recycle it
Getting Beast Souls from Shadow Souls:
There is a temporary mount and a permanent mount available when doing Tower of Kings. You may exchange 800 Shadow Souls for the Netherwing Dragon. If you have already activated this card, you may recycle it for beast souls.
Getting Beast Souls from Mystery Stones:
Killing monsters, elites, and bosses in Wilds drop Mystery Stones often. 1200 mystery stones can be exchanged for the Majestic Stingray mount. If you have already activated this card, you will get 160 beast souls for it.
Getting Beast Souls from Game Events:
Events like Cross Server Guild Battle and Chaos Wars have mounts in their shops to exchange for. Depending on the mount, if you have already activated it, you can get between 80 and 180 beast souls!
Temporary mounts cannot be recycled for beast souls and not all permanent mounts can be recycled.
Getting Beast Souls from Event Chests:
Monthly Event chests, just like the Beast Souls Chest, may drop beast souls. The following link shows an example of drop rates from event chests.