When playing on Hard Mode, you will want to equip 2 mastered HP UP materia to each party member. This will raise the HP of party members as far as possible.
You will also want to equip a mastered Chakra materia to every party member, and a mastered Prayer materia to 2 party members. In Hard Mode you can't use any items; this means you can't use items to restore HP. If you use curative magic spells you also run into the problem that your MP depletes without any way of easily restoring it (again, as you can't use items). Chakra and Prayer materia then prove invaluable as they let you restore health without using MP.
I find Cloud's Triple Slash ability is effective for quickly dispatching opponents when you're facing more than one enemy at once.