If an investigator is engaged with a snake and then receives ichtaca if they fight the snake will ichtaca attack?

Is there a reason you think she would? If I remember right, she has Alert, Retaliate, and attacks if you fail her parley. Attacks of opportunity only trigger when you perform an action that is not a fight, evade, resign or parley unless there is some other factor.

Retaliate and Alert only trigger if you fail the check against the enemy that has those keywords. I don't see why Ichtaca would attack you for performing a fight action against another enemy.