Stats of Archer Tower
An Archer Tower has 1800 base HP and 1450 base Ranged Attack Distance. If your target is a Downtown, its Level 10 Engineering and Archery will increase Archer Tower's HP to 3600, and Attack Distance to 2175.
Choice of Army Units
Be sure to use Ballistas, Catapults or, at least, Archers. Melee units like swordsman and Light Cavalry stand 0 chance of prevailing over Archer Towers.
Ballista, whose Attack Distance can mount to 2400 in the condition of Level 10 Archery, is your best choice. Even in a war with a Downtown, they are still able to inflict damage on the enemy's Archer Towers while they can't reach you.In addition, when Archer Towers and Ballistas are at fire with each other, the former's Attack is discounted by 80% while the latter can exert 10 times its Attack ability.
Due to the huge production cost of Ballistas, Catapults could be another option to deal with Archer Tower. Level 10 Archery can boost Catapult's Attack Distance to 2100.
For instance, a Downtown is fortified with about 5500 to 6600 Archer Tower. With Level 10 Battle Skill and a Hero with high Courage and Leadership, you will need some 40,000 Catapults to instantly destroy the towers, or some 20,000 Catapults to get rid of them over the time.
Archers are not recommended to tackle Archer Towers, for their HP is only 1/2 of Catapults and Attack is even lower. Unless the enemy has low-level of archery and wall while you have max archery.
1. The instance Archer Tower enters the range of your Ballistas (or Catapults, Archers), switch them to Defend and aim at the Archer Towers.
2. Line up your melee units one block in front of the Ballistas to protect them from the enemy's charging units.