crash log say your EntityPlayerSP is modified. That mean some MOD is conflict with PlayerAPI.
Mandatory member method "api.player.client.ClientPlayerBase getClientPlayerBase(java.lang.String)" not found in class "net.minecraft.client.entity.EntityPlayerSP".
There are three scenarios this can happen: * Minecraft Forge is missing a Player API Core which Minecraft version matches its own.
Download and install the latest Player API Core for the Minecraft version you were trying to run.
* The code of the class "net\minecraft\client\entity\EntityPlayerSP" of Player API Core has been modified beyond recognition by another Minecraft Forge coremod.
Try temporary deinstallation of other core mods to find the culprit and deinstall it permanently to fix this specific problem.
* Player API Core has not been installed correctly. Deinstall Player API Core and install it again following the installation instructions in the readme file.