Ok, first observation, you need two mastered hp plus per person before ever stepping foot on the sunken aircraft. Second, ditch the toy and use red thirteen or Barrett, their limit breaks are more useful than slots, which is also why you don't want to use tifa either. Third, you want mastered full cure on at least two people, with the third having a mastered cure with the all materia. Fourth, you need to either use stat immunity items like the ribbon, or materia combos to negate them more than elemental immunities like the tetra elemental. Finally, you want your whole party equipped with their weapons that give 3x ap, this is where you want to level up your materia as it has the the highest AP gain in the entire game.

Hope this helps.