Alternatively you can choose the bus, which is servicing around the clock.
Exactly out of departure area you can get the bus X95 and get off at Syntagma Square (last bus-stop).
When you will arrive at Syntagma, you can choose either metro line 2 until Omonoia station, either to get a local taxi.
Attention! Pay to the taxi only what is written on the taximeter (minimum tariff is 3.20 euro).
Usually the way from Syntagma to Achillion Hotel is not more than the minimum tariff.