When a young psychic girl becomes the victim of abuse she must use her ethereal powers to stop the horror and find a path to normality.

I agree, this logline is too vague, but I find the concept interesting and hope you post a revised version.

The nature of the initial abuse is important as it is the inciting incident; was she tortured, mutilated, raped? This is the event that motivates her to take action and therefore the more sever the abuse the more powerful her actions.

Your log-line seems better but instead of using "horror" you can use "abusement". And you should specify in your script how she got those powers.