Yes, it’s possible. Get the SeaJet ferry from Athens to Mykonos. It should arrive at 9:30am or shortly after. You’ll have to hurry to store you’re luggage at the Sea and Sky travel agency across from the Old Port and then buy tickets for Delos. The last ferry to Delos leaves at 11am or maybe 11:30am. Ferry to Delos is about 30 minutes. Last ferry back is at 3pm which will give you plenty of time before the last ferry of the day to Naxos (at 6:15pm on SeaJet). All the ferries mention here use the Old Port. Don’t book any ferries that use the New Port or you’ll have trouble making the connections.
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