A performance can only be deleted if there are no tickets attached to it.
If there are tickets attached to the performance you want to delete, first you need to click into the tickets and click the delete button to delete the ticket. You will only be able to delete tickets if non of the tickets have been sold and there are no active reservations on the ticket. If you do not see the delete button on the ticket then you won't be able to delete it for the reasons outline above and therefore the best option is to change the performance status to hidden so that the performance is no longer available to customers.
Once you have deleted all the tickets that are attached to the performance, you should find yourself on the performance management page. If you refresh the page, the Delete button will appear in the top right of the page and you can then delete the performance.