Also, here is the law itself in case you want to read it (articles 111 to 114, also in Portuguese): http://www.legix.pt/Portals/3/docs/CT09-23_Jul_2012.pdf
The typical way to hire full-time workers in Portugal is indeed a full-time contract with an experimental period (EP), what Vasco colloquially called an "at-will" period. These contracts are called "por tempo indeterminado" (or sometimes "sem termo" or "com termo incerto"), which means "for an indefinite period". The EP can last between 90 days (3 months) and 240 days (8 months) -- non-managerial roles get 90 days, which is what Andreas had on his contract (shorter durations benefit the worker). After the EP is over it is VERY hard, from a legal standpoint, to fire a worker, which is why the EP exists in the first place.
During this experimental period, the employer can terminate the contract with no advance notice and paying no compensation for the first 2 months. Between 2 months and 4 months (if the EP lasts that long), the employer must warn 7 days prior, or pay 7 days of salary as compensation. After more than 4 months, and until the end of the EP, it is 15 days. The worker can always terminate the contract with no notice during the EP. After the EP is over, the worker must provide 1 month of advance notice to terminate the contract, and the company usually cannot fire the worker at all.
According to Andreas' original post, he was fired after 1 month, during his EP, which means he is entitled to no compensation. Unbabel paid two extra weeks of salary (Andreas admits that in his blog post), which shows that they treated him better than the law requires. If indeed he was also paid $1000 extra (from Vasco's post), that is even further above what the law requires.
Andreas' blog post suggests that he thought he had a 3-month contract, which he did not. Legally, he could even be fired after 1 day on the job, and get paid 1 day and nothing more. While Unbabel may be slightly guilty of not explaining correctly what Andreas signed, I still believe that Andreas has the majority of the blame for not understanding what he signed or searching around what are the typical work laws in Portugal. Heck, if I went to Sweden, I'd ask for an English translation of the contract from someone outside the company, even if the company itself provided an English translation. What happened with the landlord seems to confirm this, since he had the legal right to stay for as long as his deposits lasted, and simply calling the police (no need for a lawsuit) would ensure that he could stay until his deposits ran out. It is, again, very hard to evict a person just like that.
In summary: Unless I'm missing something here, Andreas was treated considerably better than required by law and has no legal grounds for complaining.