Open all year, here you can find the nearest supermarket to where you are staying. Get to know your local shop keepers for your essential supplies especially if you are staying in a holiday home rental on Hydra Island Greece. They all deliver by Mule!
When I first came to Hydra in 2000, there were only two supermarkets in Hydra Town. Today there are four to choose from, and often islanders will buy a bit from each depending on what each have in at different times and after price comparison. In Kamini, there are four supermarkets although they would be described as general provisions shops elsewhere.
Generally the supermarkets will stock what you would expect most supermarket chains to offer elsewhere in the world except the range and volume they hold is less as the premises are very much smaller. (Building restrictions on Hydra, as it's designated a national monument, prohibit the building of larger properties.)
Be aware that brand names that you might recognise, such as Heniz Baked Beans, will be a lot more expensive than the local, and equally as good, variety of tinned beans. This is because they are imported. Similarly, it is less expensive, and a much tastier option, to buy cheese from the block at the delicatessan counters rather than pre-packed options.
I don't think there are any supermarkets on the island where the staff don't speak English so if you can't find something, just ask.