A short explanation to the goals of each mission in the Greek campaign and a viable tactic of reaching them. Support by a video series.
Mission 1: Claiming Territory
Claiming Territory is, like most starting missions, fairly straight forward. Your objectives are to destroy the Pelasgian farms and to build 5 farms on your own.
The mission starts off with only a few militia and villagers. The best position to start is directly to your right. Walk down along the water and eliminate the yellow opponent (Danaans) quickly. This serves as both a good starting position and it quickly takes an opponent out of the game.
Once you have done this, go ahead and build a town center and develop your economy. To fulfill your first objective, you have to build 5 farms. For this, you must gather enough food to go to the 2nd age (Tool Age) and build a market. With that, you can build farms. Farms will also be required to sustain a longterm food production.
The second goal is a bit harder. You must destroy all Pelasgian farms. This practically pits you in a direct war against them. The Pelasgians are located in the west of the map. Make sure you have a good economy to support constant unit production, then build up a diversified army and replenish your losses while attacking them. Once you break through their defense, you can easily go ahead and kill the farms.
Mission accomplished.
Mission 2: Acropolis
In the mission Acropolis, your objectives are to capture the ruins and build 2 sentry towers next to the ruins.
This mission starts off like a regular random map game. Build up an economy quickly and make sure you develop your base nicely.
The first important step is to quickly establish a base in the middle of the map where the gold piles are located. Quickly attack it and build up military buildings to produce units from. A dock and war ships can support the position nicely.
Once this position is set up you can continue developing your economy and either go for a full out attack on your opponent or go to the Bronze Age. Both are viable ways.
Use your superior economy to push through their defense and take down their production buildings while raiding their economy. Once the enemy is mostly dead, you can free your way to the ruins in the top of the map and destroy the towers next to them. Replace those towers with towers of your own and win the mission.
Mission 3: The Conquest Of Crete
In The Conquest of Crete, your objectives are to capture the artifact and destroy the Minoan temple.
The mission starts off by placing you in the yellow base (Minoans) with 4 Archers and 4 Cavalry units. Forget about the archers that your screen starts on, they are dead. Grab the horses to your right and run for your life. Follow the path off the hill, then head to the south of the map while trying to avoid as many opposing units as possible.
The video shows what I found to be the most suitable path.
Once you are in the south, you are given a base. From there on, it is for a while the standard base developing while defending your base.
You start with a small army that you can use to go up the left side and secure additional ressources. Your main goal here is to secure more gold piles. You need additional gold to build valuable units such as cavalry, hoplites and catapults.
The next step is to eliminate the Minoan Scouts in the West to calm the game down further and secure map control and additional ressources. You can then build up and army of your choice and grab the middle of the map to secure an entry way to the hill you first escaped from. From there on, use the army along with several catapults to attack the towers on the hill.
Once the hill is taken, proceed to fulfill your objectives and grab the artifact aswell as destroy the temple.
Mission accomplished.
Mission 4: The Trojan War
In The Trojan War you must slay Hector and Paris. You must also capture the treasure of Priam.
The mission starts off in a fairly regular way. You start on an island and your first step is, as usual, building up your economy. At the same time, start building warships to secure the water in front of your island early on.
Control over the middle sea and islands gives you great access to the southern and eastern part of the map which is where the Trojan opponent is located.
Clear the coast in the south with your ships and then establish a base there to replenish units in front of the enemy. Defend the incoming attacks with your land and water units and then destroy the opponent base. The 2 Heroes are protecting the artifact. As soon as you get close, you will be able to lure them into a fight and hopefully kill them
Now all that is left is to go for the artifact and the mission is won.
Mission 5: Colonization Of Ionia
In Colonization of Ionia, your objective is to destroy the Luwian Government Center.
Your start off on a small island with very little ressources. Gather wood to improve your fleet and gather food with fishing ships. You can trade off a bit of wood to Athens right to the left of you.
Once you have a few more galleys, head to the north and destroy yellow docks (Aegean Pirates). You can then land your swordsmen and take their islands to gain access to more ressources.
Once the Aegean Pirates are defeated you can establish a base and an economy on their land. Their main base has direct land access to the Luwians.
Develop your economy and go to the last age (Iron Age). Then go for a strong attack with a well developed and fully teched army and take down the three government centers.
Mission 6: The Siege Of Athens
In The Siege of Athens, you must Capture the Spartan baggage train. It is represented by four artifacts.
The mission starts with a fairly well developed base that is being attacked by the Spartans. Don't get fooled here, you can't defend the base. Make a run with all your villagers and whichever units you can grab and transport them away. You can meanwhile use your warships to harrass the Spartans but you will not defeat them right there.
Transport the villagers to the right edge of the map and build a town center to establish a base and economy.
Once you established an economy, make sure you get up a sizeable navy to controll the water in the middle. Once you have the water under control, use the ships to patrol the coast and weaken the Spartan army on land. Also make sure to destroy the Spartan Navy which has its base located in the south. You can use ships to surround and kill them.
Now you can use an army of Centurion with support of your ships to kill the Spartan army and take control of the artifacts which will win you the game. It's highly likely if you cleared the map beforehand and you killed the Spartan army that you won't even get to obtain the artifacts as you win by eliminating everyone.
Mission 7: Xenophon's March
In Xenophon's March you have to capture the artifact and escort it to your government center in the north of the map.
The mission starts off with a small but powerful army and a couple villagers. You can use your priest to slowly march forward and grab single enemy units. Engage only in small fights that assure limited to no losses. Then heal your army back up.
Progress through the map and establish a small economy with your villagers.
Once you reach the first river you can build a few war ships and clear the coast without any real cost as you have enough spare wood to gather. The ships can kill most of the yellow opponent.
Once you reached the yellow main base you can grab the gold located there. After breaking through the brown wall you can find friendly catapults right below.
Shield the catapults with your Centurion and grab all the gold you find on your way. You are now powerful enough to engage in any fight so you can march forward and attack on sight. Once you reach the end you have to get across the sea to the artifact.
The easiest way of getting across is building a sneaky dock (good position shown in the video at 47:28). You can build a few warships there and convert enemy warships to aid your cause. Then clear the sea and bring the artifact to your government center.
Mission 8: Alexander The Great
In Alexander the Great you have to defeat all enemies and destroy the wonders they attempt to build. Then you have to build your own wonder in the marked area.
The mission starts off on a very small body of land with a small base but a strong army in place. You also have villagers located in the west. Use them to set up an additional base for a strong economy throughout the game.
Use your early army to secure the position and ressources just across the river. Establish your main base there.
As you can see, there is already a wonder timer ticking down. You have very little time to destroy the wonder so prepare for it quickly. Build siege weaponry and hoplites early to make a quick push. Beware of raiding attacks in the meantime so to be safe, you can keep a few hoplites as defense.
Your attack on the wonder will be keyed by your early army as it contains strong units. Charge with the support of a catapult and destroy the wonder.
Once the wonder is destroyed, you can shortly get into a more defense position and build up your economy. Use that to train a well developed and strong army and clear the map progressively to make your way towards the marked area.
To finish the campaign, place a wonder in the area.
Source: https://gameplay.tips/guides/5114-age-of-empires-definitive-edition.html