Heavy Cats can be researched once both Catapults and Siegecraft are researched in the SiegeShop. The unitz a Hittite must utilize and what to avoid. When playing this way it is important to keep your HHA behind your catapults and let them kill any ground units that approach your catapults. As they approach let your HHA fire at them while your cats continue to attack other units such as but not limited to enemy catapults, towers, buildings. Sometimes it might be a good idea to withdraw your cats if it is obvious the enemy will overwhelm you.
Elephants are a feasible unit to take advantage of also.
There are two main uses for elephants. The first being an initial strong rush of elephants. The reason elephant rushing can be effective is that elephants require no uprades. They are able to attack immediately. But there is such a thing as to much of a good thing.