Sort them by date, say newest first. Scroll down to the first one you want to delete. Select it. Now use ctrl+shift+end to select down to the bottom of the list. Now the delete button will delete all the selected messages.

The Expression Search GmailUI addon gives you finer control. It could allow you to display all messages before a certain date, or in a given date range, or messages to or from specific correspondents, or with or without attachments. Then ctrl+a would select all the visible messages, and again del would slay them all in one action.