Hi Cephas,
For POP3, the option to "delete mail once downloaded" is handled by the server. You won't see such an option in Aqua Mail.
In order to set this up, you need to enable the setting on your mail provider's website, then you'll likely have to re-download the messages with Aqua Mail so the server deletes them.
However, I don't recommend this approach for the following reason: You cannot export your messages from Aqua Mail. This means that you, eventually, will lose this mail. Whether it's by changing your phone, by factory resetting or by uninstalling Aqua Mail itself.
If you don't mind the server space being taken up, I'd recommend leaving the mail there. Alternatively, a good way to backup mail are desktop mail clients. Those usually have more robust options related to POP3 mail and storing/archiving of messages.