You cannot upgrade a "basic" ticket to regular business class.
What you can do, if you want to risk it a bit (because changes cost their own fee and it isn't a low one either) is to try and change the ticket for a date as far in the future as possible (I mean something like over 9 months in the future at least) and then hope that Aegean changes the flight schedule by then, so that you will be entitled to a free cancellation and full refund of fare+taxes (the change fee will obviously not get refunded).