If you, or at least one of you, are baptized into the Greek Orthodox Church, (and even if the other is Catholic), then you may marry in church in Hydra. You will need your baptism certificate and a letter of reference from your local priest to the priest marrying you in Hydra.
Those who have been divorced may also be married in a Greek Orthodox church and must have their divorce papers as well as the religious dissolution of their previous marriage papers.
In addition to the Church Documentation, you will also have to provide exactly the same documents as you would for a civil marriage.
There are lots of different Greek Orthodox Churches in Hydra where you can get married. BUT, please note that you CAN'T get married in the Cathedral Church of the Assumption of the Virgin Mary in Hydra port because it is designated as a monastery, where only baptisms and funerals can be conducted. Similarly you can no longer get married at the little chapel on the small islet off Kamini Beach.