Perseus and Medusa
Calydon - the dirty way
Now this is a down and dirty method of doing this mission.
Come into the colony with as much money as possible, at least 20k would be ideal and possible. Build housing (about half way to the left side of the screen) with just medical support and Maintenance. Get wine production up and running as soon as possible. Build a City Palace as far to the right as you can get be sure to put a wall around it with plenty of room for a Hero Hall (don't forget Maintenance Officer inside). Make sure you have storehouse for gifts of marble, to store wood, which you need to cut, and statues. Do not trade yet except for 2 statues. Trick to saving money on trade is to set storehouse to accept 1 statue and only request 1 statue. Wait until the next year to accept 1 more statue. Fill two storehouses with wine. Don't worry about messages saying not enough food. This down and dirty we aren't going to feed these people. You will have to pay at maximum two bribes to keep from being attacked (wait to build your palace until you've paid the first one). Add housing as needed to keep everything fully staffed. When the monster comes on scene you should have enough of everything to summon him. Then build the Sanctuary, you should have enough extra workers to do the job. Remember only buy 1 statue at a time. Think the total number of statues needed is 4 plus whatever the hero needs.
Summon the hero and let him do his thing. As soon as he's summoned start trading wine as fast as you can. Meet whatever other requirements needed to complete the mission don't leave the mission until you have earned enough money trading. The best amount of money to have on leaving the mission is close to what you had on arrival.
This is not a nice way to play this mission but it does work well.