I got a lot of helpful advice from Ben6600, here is our conversation and I hope it helps you too
"Hi,
First I registered at the aan.pt 1 website
https://www.aan.pt/subPagina-AAN-001.005.005-aeronaves-nao-tripuladas-drones
To get the account approved I had to download a Declaration form, sign it and post it to the AAN in Portugal. This can be avoided if you have a certified digital signature. My account was approved within a couple of days.
I then applied for the European Operator/Flyer certs. I did this via the Irish website, which turned out the be fairly expensive, so I would recommend doing this via Luxembourg. This stage did require that I install an authenticator app, which was slightly long-winded but got there in the end.
The aan.pt 1 website portal is very friendly and you can add dates and locations of where you intend to fly. As long as the areas are not sensitive, approval is given instantly and you get a certificate you can print and carry with you.
Hope this helps.
Ben
To be honest the Luxembourg system did look more complex, which is why I went down the Irish route. To warn you, it cost 30 Euros to take the test (which I didn’t discover until I’d completed it) and 30 euros to get an EU Operator ID. I didn’t complete the process in getting a Flyer ID as time ran out and I suspect it would cost yet another 30 Euros."
Please contact Ben6600 or scroll down in the topic until you find the conversation between Ben and I.