So, I've been trying for a couple of days to make this integration work, and I feel I'm almost there. I managed to create the issue and then create the temporary attachments through the REST API, unfortunately when it comes to creating the permanent attachments on a issue I keep getting 404 error, saying that my issue was not found.
I'm following the documentation path, being:
POST /rest/servicedeskapi/request/{issueIdOrKey}/attachment