On the iPhone you can open your mail app, select the email and open any mailbox you want to edit, tap edit on the top right , select the emails you wan to delete or select all and then tap delete on the bottom right. In my opinion the best way to do it is online, just go to your email login website log in and select your emails and delete them, usually you can delete emails in bulk even the whole content of a mailbox, usually you can right click on the mailbox and select the action you want.
Delete emails on your iPhone or iPad – Apple Support (UK)