Your Special stat solely determines the power of your special attacks. The more points you have allocated to Special, as well as accessories that increase Special, will allow you to deal enough damage to surpass their defenses. When a stat is maxed out, it gains a bonus, so completely allocating points to Special will increase it's effectiveness even further.
Thankfully, you can reallocate stats at will at every checkpoint, so when you get to a part where you need high Special, put as many points as necessary into Special so you can complete that section.
In the future, I recommend investing in accessories that increase Special, so you don't have to worry about Special and can focus on Attack for normal damage, Defense for survivability, or Agility for evasion and critical chance (Accuracy is either a flat percentage, or might be modified by Agility, but I'm not sure).