During the fight, you should keep a distance from Char at all times. The amount of damage you deal is determined by the amount of flames you have lit (maximum of 100 damage allowed to be dealt to her per flame). As you fight her, keep lighting flames. Keeping at least 5-10 fires lit will ensure adequate damage against Char. A good strategy to make many fires is by putting your pitch can on your action bar, lighting flames while running around.
The higher your life points, the higher Char's max hit is. Some time in the fight, she will summon flame walls which you can avoid by maneuvering through the gaps in the walls. While she is enraged (glowing), she is invincible for a brief period time in which case is an opportune time to light more flames.
Take the journal. (2•~)…
That's a good idea.
Climb down the steps to enter Char's lair.
Talk to Char to engage the fight.
After defeating her, finish the dialogue. (2)…
How do we get out?
There may be a glitch where you can not finish the dialogue, in that case leave the cave through the southern tunnel and come back in.