There's no batch processing available currently but using inline moderation will work.
One way to make this a bit easier on yourself (and your sanity) is to increase the number of media items shown per page, then you might be able to get through a big batch of media by clicking an inline mod checkbox, clicking Select All, then selecting the Move action from the inline moderation drop down.
If you have thousands of media items, the above suggestion probably won't be too appealing.
I could reluctantly advise on doing it via database query if you can't feasibly do it any other way. This isn't perfect though because it would leave the category counts incorrect (but there is a rebuild for that).