The director hits with high physical damage and high fire damage. You might be better served giving Griss a shield with fire protection. Let her be the chew toy for the Director. It's a good tactic for a lot of tough enemies. Let a defensive focused Griss take the beating while you deal out damage. That lets you focus on using attack potions while letting Gris focus on healing.
Ideally if you can get Griss' fire resistance to above 100, that will take the heat of his fire attacks. Fire resistance potions are your friend. So are shield potions.
Before you start the fight, a summon wolf adds a little flexibility. If it get hit, it won't last long, but any damage it does helps, and any damage it takes, is less damage for you to take. The distraction for the boss can buy you enough time to for potion cool down to pass.
I also note you don't have any ice weapons. Ice weapons do extra damage in this fight.
Keeping the theme of giving Griss a sheild, if you give her an Icicle, she had a pretty good damage output against the Director.
It's tempting to give Gris a 2-H weapon early on. She can do decent damage with it that will help clear out dungeons a little faster. However, you're going to come across a few enemies that require a little more durability to beat. Hence, even if you make Griss a 2-H weapon user, it's good to keep a spare shield and 1-H / Light weapon.