We are on a cruise in May and will be one day in Athens on 29th. How far in advance am I able to buy tickets for the acropolis? As of March 12 I am not able.
You will be able to buy your tickets from April 1, when the system switches to summer pricing.
When booking you will have to specify a visit time slot and respect it.
Ticket purchase is here:
https://hhticket.gr/tap_b2c_new/english/tap.exe?PM=P1P&place=000000002