I have found cats normally go for the eyes first.

I've posted this one before... the best trick I ever saw in a cat fight. 8PM... Cassie (4 years) ambushed Cheucie (12) at the LR/KIT entrance and immediately dashed down the hall, with Cheucie in pursuit. Cassie planted her front claws in the carpet at the bedroom door jamb at the end of the hall and put the top of her head against the jamb. She then levered her hind end up just as Cheucie caught up to her and raked Cheucie's chest and neck with her hind claws in whirlwind fashion a la Bug's Bunny cartoon speed. FUR was FLYING!

I let out a great roar and the fight was over... for a while. Cheucie immediately went to the litter box in the basement and then sat in the kitchen by the food and water dishes. At 2AM, I heard them at it again and the next morn, the was fur in the kitchen... Cassie's.

Cats can be pretty cagey.