New update

do you know how the contest is calculate ?

I wonder if the stars of the country affect the score. And does difficulty matter? (Ex: Easy/Medium/Hard)

With these new generals and a long time of upgrading units, conquests are faster than ever. Yelu Dashi is literally a troll general; skipping would-be enemies and taking out cities in no time. When I get around to redoing conquests to boost my score, it'll probably be the highest it'll ever be.

lol
I mean in conquest how the points are earned ?

stoic , yep, mine is higher. IAP privileges are strong in Conquests...

In case You have all IAP the problem is most likely in the strategy You use.
For normal conquests turns (used for completion) is the most influencial part of what the score You are going to receive. The highest coefficient is for 1* country. So in case You need highest score play 1* country and complete it as fast as possible.
In order to complete it fast You need to manage 2 things carefully.

1) Diplomacy. Use best possible consul right from the start.
Here is my consul, I assume he is the best one with this gems setup.




Additionally I deploy him on 1 unit to leave him in the capital to boost my income.
Right from the start You normally need to complete all possible missions that reward You with resources (like build houses and other stuff). With these resources You will immediately research diplomacy technologies. This will make Your conquest faster as You can avoid fighting most of the enemies especially if they are on the opposite side of the map. So just keep playing and defeating nearest enemies and wait for the relations with others to grow naturally. If someone You don't want to fight asks You to attack another country You don't plan to fight as well, immediately ally the country sent a request and reject. This way You will lose the relations but it doesn't matter anymore as You are allied. So keep some money in safe for this always. And apparently agree to attack the countries Yoh plan to defeat even in case You are not going to do it right away. It's free money.

2) Movement. You simply need to use generals with forest and mountain movement. Archers are the best for conquests as generals with units providing Your legion with Mobilize and Repeated fire are great as they can conquer cities much faster. More archer with Mobilize+Repeated fire combo and You are good. Just use units like Woad raider and Ravenna crossbowman and You have this combo and forest/mountain movement at the same time. Best setup for conquests.

PS: Challenge conquests is different story. Diplomacy is almost useless. I managed to ally Byzantium and Byzantine Expedition in the Rise of Byzantium conquests playing as Vasco, but I assume it is not possible for f2p anyway, only for IAP.