We don’t have bulk options to remove registrations as such, however, now if you delete an event EE will work through deleting all of the related data for that event, including Registrations and their transactions, payments etc.
So one option for this is to work through deleting the old events, when you trash them they’ll be ‘soft deleted’ to the trash view.
When you go to that view and click Perm Delete ee will show you a preview of the related data its about to delete and ask you to confirm. That will batch delete the details related to that event.