If you guys are unfamiliar with this, Batbale is simply another word for Christian Bale's version of Batman, while Batfleck is Ben Affleck.
Reimu Hakurei is the shrine maiden of the Hakurei shrine. She resides in Gensokyo and has powers, nothing else to it.
TLDR; Somehow Batman ends up in Gensokyo and decides to fight Reimu, who wins and if Batman, which adaptation?