From the train station its easy to do. But to get to the train station from the port is a very long walk. See the google satellite map by going to googel maps and searching for "athens map ???????? @37.948089,23.642557" I tried to paste the URL but it was too long. The cruise ships dock at the south end of the port and the train/metro station is the Square M symbol top right end of the port. We walked it but it was a long hike. I suggest a taxi to the train station or a bus to the train station. There are 2 stops on the metro line that will be close to an entrance and one that will make you walk all the way around it. At the train station you want to take the green line and then transfer to the blue line at the Monastiraki station (You can get off the green station at Thissio and be close to an entrance but it is on the far side away from the Acropplois itself.) You then want to get off the blue line at the Syntagma station and get on the red line to go one more stop to the Acropoli station.. this will put you at the main entrance with minimal walking. IF you don't want to do so much transferring, just stay on the green line to the Metaxourgio station where you can transfer directly to the red line to the Acropoli station. See a metro map here.
Of course you will want to by an "all day" metro pass since you will want to get back to the port and use the metro to get around.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013