To delete many Payment Types at once, hover your mouse over the Manage button in the header menu.
A drop down list will appear.
By selecting the option "Payment Types", a new page will open up with a list of all your Company's Payment Types.
Select the Payment Types you wish to delete.
On the top right hand side of your screen, to the left of the export button, is a smaller button marked with an ellipsis "..."
When you select the ellipsis "..." button, a drop down list will appear with a single option "delete selected".
Once you click this button, all the selected Payment Types will be deleted.