Hi Krzyten,
Welcome to the Apple Community.
Thank you for sharing your query with us.
Sorry I'm no expert on iPad running iOS 9. (Latest iOS is 15)
So these thoughts may not be quite right in your case.
Seems the Mail Archive folder is part of the Mail app itself, (like Trash, or Drafts etc.) so you may not be able to delete it.
When we delete an e-mail, it depends on our settings whether either of two choices happens:
(1) send the eMail to the trash / bin, (eg: may be deleted after 30 days, or never, if that is set.)
or
(2) archive the email in the archive folder. (stays there without being deleted, until we move / retrieve it).
If the archive option is turned on:
to delete an email instead of archiving it, touch and hold , then tap Trash Message.
To see your settings:
Try going to Settings > Passwords & Accounts
Tap your eMail account
Tap Mail
Tap Advanced
Now you should see (and be able to change) whether deleted mail goes to Trash or Archive.
This article was written for iOS 12 ... so it may or may not not apply to iOS 9
Delete and recover emails in Mail on iPad – Apple Support (AU)
All the best :-)