You can base64 encode your username and password.

This is generally used with what’s know as Basic HTTP Authentication (or basic auth) and will send the API a username/password or a clientId/clientSecret combination that is encoded using the base64 method.

Your API docs may include something that looks like below:

Authorization: Basic <Base64 encoded username and password>

To use this within WPGetAPI you simply need to add the details into the Headers section as shown in the image below.

By adding the base64_encode() function, the plugin will automatically encode whatever is in between the brackets. It is usually a username and password separated by a colon like so: username:password