Spiders huge and vehement enough to eat bats exist, and they exist on every continent save Antarctica. Spiders won’t generally feast on bats, but if they get to lay their hands on one, then sure! why not? While it is fairly common for spiders to dine on frogs, they have often been sighted having small birds and even snakes for dinner.
While bat eating spiders are not really new, researchers have realized that such cases may be way more numerous than previously thought. Turns out, web-building spider species (Argiope savignyi) and a tarantula species (Poecilotheria rufilata) do quite enjoy their bat meals. Of course there are more species that like to hunt, like some of the huntsman spiders, wolf spiders and related species.