Unfortunately, there is a lot of truth to the claim. I wouldn't call it entirely accurate, but I wouldn't call it false either.

Xenios Zeus

"Xenios Zeus" is a large scale police operation, targeting illegal immigrants in Attica. It started on August 4, 2012, is ongoing, and has not extended to the rest of Greece. The Ministry of Public Order & Citizen Protection published regular reports for the operation until February 22, 2013 when they abruptly stopped (without - as far as I know - any explanation). Up until that point the operation's statistics where:

The Police operation was officially launched in August 2012 and the Ministry of Public Order stopped publishing data in February. The report states that of the 84,792 people investigated as part of the Police operation, 4,811 (about 6%) were found to be in Greece illegally and only 59 were arrested. Source: Human Rights Watch condemns Greek Police and ‘Xenios Zeus’, Το Βήμα, June 12, 2013. The Greek version of the article goes into a bit more detail.

According to a different source, the numbers are much higher:

The Greek police force says its crackdown on illegal immigration, which has led to almost 6,700 people being detained and just over 1,500 arrested since last Saturday, is already producing results. Authorities said the number of migrants entering Greece via the country’s Evros border with Turkey has fallen dramatically. According to figures released by the police, 447 undocumented migrants were caught crossing into Greece illegally on August 2, before the Xenios Zeus operation began, but on Wednesday and Thursday this week that figure had fallen to 12 and 15 respectively. Source: Police claim Xenios Zeus operation a success, Καθημερινή, Jul 3, 2013.

Both sources are major - and generally reliable - newspapers. The discrepancy in the numbers is not surprising, the first source quotes official data up until February 2013, the second reports estimates for the whole operation. The numbers skyrocketing after a certain point is not surprising either, the operation intensified significantly once the first detention centers for illegal immigrants were completed.

Detention centers for illegal immigrants

The first - and larger one - opened in Amygdaleza in late April, 2012. There are at least four more, in Corinth, Evros, Rodopi and Lesvos. The Amygdaleza camp was build specifically to host illegal immigrants, the others are probably retrofitted military or police buildings (can't find reliable sources). The original plan for 30 camps in total is currently on hold, due to protests of the local populations and lack of funds.

According to non official sources, Amygdaleza currently hosts 2.300 illegal immigrants. Since the Ministry of Public Order & Citizen Protection stopped publishing data, it's not possible to verify that number. Reports suggest conditions in the camp rapidly deteriorated after April, 2013, when several services were cut due to lack of funds. Surprisingly, a private security firm was hired recently to guard the camp.

Sources:

Sex workers

Prostitution is legal in Greece, and sex workers are required to get tested for STDs once a month. The tests are free and available in most hospitals.

Now, the incident the claim refers to is most likely the April 2012 arrest of 11 female sex workers. All of them were operating illegally and failed to produce proof they had been recently tested for STDs. Consequently, they were tested and - according to reports - found to be HIV positive. In an unprecedented move of dubious legality, their names, their parents names and their photographs were released to the public. A few days later, on May 5, the Ministry of Health released a report, claiming a total of 85 HIV positive sex workers have been found in 1180 random tests since September 2011. The legal framework for these checks has not been clarified (or challenged).

However, the issue was and remains highly controversial. There are conflicting reports that suggest none or only some of the women were HIV positive, and that the arrests and the release of the photos were a publicity stunt, designed to boost the ruling party's popularity for the upcoming May 2012 election. Andreas Loverdos, then Minister of Public Health, had promised a new legal framework that would have allowed a lot more flexibility for random searches to the police, and would legalize forced HIV tests during detention. Interestingly and although the government changed, Mr. Loverdos' framework forms the basis of a law currently in consideration. The draft of the proposal for this new law is not currently available, it will probably be available next Monday.

Sources:

Drug users & operation Thetis

Operation "Thetis" was a March 6, 2013 police operation that targeted drug users in Attica, and more specifically Athens' historic city center. According to news reports, 132 drug users were detained and moved to Amygdaleza, where they were cataloged (!?) and released (!?). The operation was met with contempt and ridicule in local media, and its legality and usefulness have been strongly disputed by KETHEA.

The day after the operation, an official statement verified it. According to the statement the operation was in collaboration with medical professionals from the Ministry of Health, and the detainees were collected from various places in Athens' center and were in need of medical attention.

Sources:

Transgender people

The Transgender Association claims that transgender people were regularly harassed and detained without cause in Thessaloniki, from 30 May 2013 and onwards. The report on GRReporter translates parts of the association's complaint and matches similar Greek language reports in local media:

The police in Thessaloniki has been carrying out a series of ungrounded arrests of transgender persons as stated by the Greek Transgender Support Association. "According to written complaints filed by our members who live in Thessaloniki, it is clear that from 30 May 2013 onwards, the police have been carrying out purges and arrests of transgender citizens on a daily basis. The same complaints state that those arrested are being taken to the police headquarters in Thessaloniki in Dimokratia Square, where the victims are waiting for at least three or four hours to be identified under the pretext that the authorities should establish whether the particular person was not a prostitute," reads an address of the non-governmental organization (NGO). The Association stresses that the police behaviour during the arrests was offensive, humiliating and that it was intended to undermine the dignity of transgender persons. In three of the complaints, the victims note that traffic policemen had stopped transgender women while they were driving their cars without any proof or suspicion of any fault or violation of the law. Later, they were taken to the police station in order for their identity to be verified. The testimonies of a large number of victims suggest that before being released from custody, the policemen threatened transgender women, warning them that if they did not "return to normal", legal proceedings against them would be initiated for indecent behaviour in public places. The Greek Transgender Support Association connects the campaign against transgender persons with the recent actions of some municipal representatives and the church against the forthcoming gay festival Thessaloniki Pride, which will take place on 14 and 15 June this year.

One notable event was the detainment without cause of Ms. Electra-Leda Koutra, a lawyer visiting transgender clients held in a police station. The Thessaloniki Bar Association corroborates Ms. Koutra's story.

A response to the complaints by Nikos Dendias, Minister of Public Order & Citizen Protection, acknowledges 720 searches that lead to 271 detainments, from June 1 to June 9. It also mentions that the officers responsible for Ms. Koutra's detainment are under investigation.

Sources: