Cataphracts are the mounted front runners among all troops. Their default behavior is to seek and destroy defenses. With a large amount of hitpoints, they can endure more than any other troop of their age, as well as dealing a lot of damage before falling. But as most troops in Classical Age, Ballista Towers can make short work of them.
Cataphracts have a lot of health but are slow and have low attack power, so use them in groups.
Cataphracts are weak against many defenses grouped together.
Due to their high health, Cataphracts can be use as meat shields to protect infantry from the defenses.
Ballista Towers can destroy Cataphracts easily like all heavy cavalry. If you can, try swarming it with heavy infantry or ranged infantry to destroy it quick enough since the ballista tower is slow.
When pushing for trophies, you would need to destroy the Town Center. In many bases, the town center would be in the center of the base. First, train up an army of cataphracts and a wall breacher such as a wall miner. When attacking, deploy your wall miner and wait till the wall miner destroys the necessary walls. Then, deploy all your cataphracts in the areas which the Town Center is more close to. If there are a few defenses blocking the way, destroy them. Then rally your cataphracts to destroy the Town Center.
Cataphracts would ignore defensive troops and would pursue their targets which are defensive buildings. However, if a defensive troop attacks the cataphract, the cataphract will attack back until the defensive troop is killed; thus making the cataphract distracted. Try to use and deploy ranged infantry such as archers or heavy infantry such as phalanxes after deploying the cataphracts to eliminate the defensive troops.
Cataphracts is a good alliance troop due to its high health; making it longer to kill them. However, they take up 6 space in the alliance gate so it cannot be used in a level 1 Alliance Gate in the Iron Age (which can only hold 3 spaces) until it is upgraded to level 2 which is available in the Classical Age.
The Reinforcements technology in the Library spawns cataphracts in the forest and they attack troops of the attacker.