What does this sentence mean?
It means someone is allowed to work now (register)
So does "Eu consegui o registro" mean "I registered", "I got myself registered"? If so Duo's translation (I got the record, but I do not work) needs to be improved.
Yes, like you got a certificate which enables you to work or even to run a company!
i reckon that: 'I managed to (get) register(ed)...' should be allowed