Don't trim away the burnt parts, just let your plant repair itself.
If you start trimming it'll not only be recovering from a 3rd degree burn, but also amputation (loss of fluid). (at least this is what I would do)

I don't know if it's possible in your setup to tie her down? Even get something small and heavy and wrap a string around it, tie it to her and get her AWAY from the lights!

Pics?